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[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question What is the length of the shortest piece to be?, think step by step [/INST] , The answer is Let us assume the length of the shortest piece to be x cm.

[INST] help me answer this question The Cartesian product A × A has 9 elements, among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A., think step by step [/INST] , The answer is A = {–1, 0, 1}

[INST] help me answer this question (ix) {x: 2x + 5 = 9}, think step by step [/INST] , The answer is {x: x ∈ N and x ≠ 2}

[INST] help me answer this question How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?, think step by step [/INST] , The answer is 3 × 20 = 60

[INST] help me answer this question For the following frequency distributions, find the mean and standard deviation., think step by step [/INST] , The answer is The mean is 90 and the standard deviation is 42.16.

[INST] help me answer this question Find the equation of the line passing through (–3, 5) and perpendicular to the line through the points (2, 5) and (–3, 6)., think step by step [/INST] This is the equation of the line that passes through the given points and is perpendicular to the line through the points (2, 5) and (–3, 6). , The answer is 5x – y + 20 = 0

[INST] help me answer this question (3) How is the solution region of the inequality described?, think step by step [/INST] N/A , The answer is The solution region of the given inequality is right to the line x > – 3, and the origin is included in the region

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Which of the following statements are true and which are false? In each case, give a valid reason for saying so.<br>(i) p: Each radius of a circle is a chord of the circle., think step by step [/INST] The given statement is false. Each radius of a circle is not a chord of the circle. A chord of a circle is a line segment whose endpoints lie on the circle, while a radius is a line segment that connects the center of the circle to any point on the circle. , The answer is False.<br>Each radius of a circle is not a chord of the circle.<br>A chord of a circle is a line segment whose endpoints lie on the circle.<br>A radius, on the other hand, is a line segment that connects the center of the circle to any point on the circle.

[INST] help me answer this question A coin is tossed three times. Describe the sample space for this experiment., think step by step [/INST] When a coin is tossed three times, there are 2 possibilities (Head or Tail) for each toss. So, the total number of possible outcomes is 2*2*2 = 8. These outcomes form the sample space S. , The answer is The sample space S = {HHH, THH, HTH, HHT, TTT, HTT, THT, TTH}

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question a17 and a24 if an = 4n – 3, think step by step [/INST] , The answer is a17 = 67, a24 = 99

[INST] help me answer this question Since, the vertices are (± 7, 0), so, a = 7, think step by step [/INST] , The answer is Comparing the given vertices (±7, 0) with the general form of the hyperbola, we find that a = 7.

[INST] help me answer this question What will Rs 500 amount to in 10 years after its deposit in a bank which pays an annual interest rate of 10% compounded annually?, think step by step [/INST] To calculate the future value of the deposit, we need to apply the formula for compound interest for 10 years, using the rate of 10% per annum. , The answer is The amount at the end of 10 years will be Rs 500 * (1.1)¹⁰.

[INST] help me answer this question Are the events A and C mutually exclusive?, think step by step [/INST] A ∩ C = {(2, 1), (2, 2), (2, 3), (4, 1)} eq φ , The answer is No, they are not mutually exclusive.

[INST] help me answer this question Solve 24x < 100, when - x is a natural number. - x is an integer. , think step by step [/INST] N/A , The answer is {'naturalNumber': '[1, 2, 3, 4]', 'integer': '...,-1, 0, 1, 2, 3, 4'}

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Prove that the expression (x + y) {mx2 + y2k (x – y)} is a factor of the expression x2k . x2 – y2k . y2, think step by step [/INST] N/A , The answer is We can prove this by expanding the expression and showing that it can be written in the form (x + y) times some other expression. First, we add and subtract y2k in the expression x2k . x2 – y2k . y2 to get x2 (x2k – y2k + y2k) – y2k. y2. From equation (1), we get x2 {m (x + y) + y2k} – y2k. y2. By multiplying the terms, we get m (x + y) x2 + y2k. x2 – y2k. y2. Taking out the common terms, we get m (x + y) x2 + y2k (x – y). Expanding using the formula, we get m (x + y) x2 + y2k (x + y) (x – y). So, we get (x + y) {mx2 + y2k (x – y)}

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Prove that cos (x - y) = cos x cos y + sin x sin y, think step by step [/INST] N/A , The answer is cos (x - y) = cos x cos y + sin x sin y

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question a^2 + 6a = 16, think step by step [/INST] , The answer is Substituting the value of b^2 from the previously derived equation b^2 = 6a, we get a^2 + 6a = 16.

[INST] help me answer this question Prove that 9n+1 - 8n+1 - 9 is divisible by 64 whenever n is a positive integer., think step by step [/INST] , The answer is Not applicable.

[INST] help me answer this question Solve the quadratic equation x2 + 3x + 9 = 0, think step by step [/INST] Comparing the given equation with ax2 + bx + c = 0, we have a = 1, b = 3, and c = 9. The discriminant (D) is calculated as D = b2 - 4ac = 32 - 4 × 1 × 9 = -27. Since D < 0, the roots of the equation are given by x = [-b ± √(b2 - 4ac)]/2a = [-3 ± √(-27)]/2 = -1.5 ± 1.5√3. , The answer is x = -1.5 ± 1.5√3

[INST] help me answer this question (iv) {a} ⊂ {a. b, c}, think step by step [/INST] {a} is a subset of {a, b, c}. , The answer is True

[INST] help me answer this question Define the terms 'domain' and 'codomain' of a relation. , think step by step [/INST] The domain of a relation is the set of all inputs for the relation, while the codomain is the set of all possible outputs. , The answer is The domain of a relation is the set of all first elements of the ordered pairs in the relation. The codomain of a relation is the set of all possible values that the second elements of the relation can take.

[INST] help me answer this question The area (ABCD) = 29 + 63/2 units², find the area of the figure., think step by step [/INST] The area of the figure ABCD is the sum of 29 and 63/2, which is 121/2 units². , The answer is The area of the figure is 121/2 units².

[INST] help me answer this question For all the values of x, the value of y would be the same in the given inequality. , think step by step [/INST] , The answer is N/A

[INST] help me answer this question Since a is non-negative, a = 2, think step by step [/INST] , The answer is Considering the constraint that a must be non-negative, we get a = 2.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Write the first three terms of the arithmetic sequence for which an = n + 10., think step by step [/INST] The first three terms of the arithmetic sequence are obtained by substituting n = 1, 2, and 3 into the formula an = n + 10. , The answer is The first three terms are 11, 12, and 13.

[INST] help me answer this question Question: P (k + 1) is true whenever P (k) is true., think step by step [/INST] Explaination: N/A , The answer is Answer: Therefore, by the principle of mathematical induction, statement P (n) is true for all natural numbers, i.e., n.

[INST] help me answer this question If f(x) = x^2, find f(2), f(-1), and f(0)., think step by step [/INST] , The answer is f(2) = 2^2 = 4, f(-1) = (-1)^2 = 1, and f(0) = 0^2 = 0.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that a^(q-r) * b^(r-p) * c^(p-q) = 1, think step by step [/INST] Using the general term of a G.P., we express a, b, and c in terms of A (first term) and R (common ratio). Then, we substitute these expressions in a^(q-r) * b^(r-p) * c^(p-q) to get A^0 * R^0, which is equal to 1. , The answer is a^(q-r) * b^(r-p) * c^(p-q) = 1

[INST] help me answer this question (ii) q: The center of a circle bisects each chord of the circle., think step by step [/INST] The given statement is false. The center of a circle does not bisect every chord of the circle. A chord that passes through the center of the circle is called a diameter, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle. , The answer is False.<br>The center of a circle does not bisect every chord of the circle.<br>A chord that passes through the center of the circle is called a diameter. A diameter is the longest chord of a circle, and it bisects the circle into two equal parts. However, not all chords have their midpoints at the center of the circle.

[INST] help me answer this question A solution is to be kept between 68° F and 77° F. What is the range in temperature in degree Celsius (C) if the Celsius / Fahrenheit (F) conversion formula is given by F = (9/5) C + 32?, think step by step [/INST] , The answer is The range of temperature in degree Celsius is between 20° C to 25° C.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question What is E ∩ F?, think step by step [/INST] , The answer is The value of E ∩ F is 6.

[INST] help me answer this question 1.(a) Passing through the point (– 4, 3) with slope 1/2, think step by step [/INST] , The answer is Given: Point (-4, 3) and slope, m = 1/2 We know that the point (x, y) lies on the line with slope m through the fixed point (x0, y0), if and only if, its coordinates satisfy the equation y – y0 = m (x – x0) So, y – 3 = 1/2 (x – (-4)) y – 3 = 1/2 (x + 4) 2(y – 3) = x + 4 2y – 6 = x + 4 x + 4 – (2y – 6) = 0 x + 4 – 2y + 6 = 0 x – 2y + 10 = 0 ∴ The equation of the line is x – 2y + 10 = 0.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Find the domain and the range of the real function f defined by f (x) = |x – 1|., think step by step [/INST] , The answer is The domain of the function f(x) = |x – 1| is R (set of all real numbers) and its range is the set of all non-negative real numbers.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question The shaded area in the graph is the required solution area which satisfies all the given inequalities at the same time. , think step by step [/INST] , The answer is N/A

[INST] help me answer this question Solve -5/4(13/b²) = -5/4., think step by step [/INST] , The answer is b² = 13

[INST] help me answer this question From the data given below, the state which group is more variable, A or B?, think step by step [/INST] To find the coefficient of variation (C.V.) for each group, we first need to calculate the standard deviation (σ) and the mean (x̄) for each group. The formula for C.V. is: C.V. = (σ/ x̄) × 100 For Group A, the standard deviation (σ) is 15.09 and the mean (x̄) is 44.6. So, C.V. for Group A is: C.V. = (15.09/44.6) × 100 = 33.83 For Group B, the standard deviation (σ) and the mean (x̄) need to be calculated following a similar process as for Group A. After calculating the C.V. for both groups, we can compare them to determine which group is more variable. , The answer is To compare the variability or dispersion of two series, we calculate the coefficient of variance for each series. The series having greater C.V. is said to be more variable than the other. The series having lesser C.V. is said to be more consistent than the other.

[INST] help me answer this question If A (4, 0, 0) and B (–4, 0, 0), find the equation of the set of points P (x, y, z) such that the sum of the distances from A and B is equal to 10., think step by step [/INST] By equating the sum of distances PA and PB to 10 and simplifying, we get the equation x – 2z = 0. , The answer is x – 2z = 0

[INST] help me answer this question Given x2/100 + y2/400 = 1, what is the length of the major axis?, think step by step [/INST] , The answer is Length of major axis = 2a = 2 (20) = 40

[INST] help me answer this question The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon., think step by step [/INST] It's understood from the question that the angles of the polygon will form an A.P. with a common difference d = 5° and first term a = 120°. And, we know that the sum of all angles of a polygon with n sides is 180°(n – 2). Thus, we can say a + (a + d) + (a + 2d) + ... + [a + (n – 2)d] = 180(n – 2) Simplifying the above equation, we get: n * [2a + (n – 2)d] / 2 = 180(n – 2) Since a = 120° and d = 5°, substituting these values in the equation, we get: n * [240 + 5(n – 2)] = 360(n – 2) Further simplification leads us to: n^2 + 47n - 456 = 0 Upon solving the above quadratic equation, we get: n = 9 or n = 16 Therefore, a polygon having 9 or 16 sides will satisfy the condition in the question. , The answer is A polygon having 9 and 16 sides will satisfy the condition in the question.

[INST] help me answer this question Does the origin lie in the solution area for the given inequalities of 5x + 4y ≤ 20?, think step by step [/INST] The origin satisfies the inequality 5x + 4y ≤ 20. , The answer is Yes, the origin would lie in the solution area.

[INST] help me answer this question Given 2x – y >1, find the region of the solution., think step by step [/INST] Putting values of x = 0 and y = 0 in the equation, we get points (0,-1) and (0.5, 0). Checking for the origin, putting (0, 0), we get 0 >1, which is false. Hence, the origin does not lie in the solution region. , The answer is The region of the solution for 2x – y >1 is the area on the right of the line graph.

[INST] help me answer this question If `f(x) = x^2 - 3x + 2`, find `f'(x)`., think step by step [/INST] , The answer is `f'(x) = 2x - 3`.

[INST] help me answer this question x + x/2 + x/3 < 11, think step by step [/INST] The solutions of the given inequality are defined by all the real numbers less than 6. Hence, the solution set is (-∞, 6). , The answer is x < 6

[INST] help me answer this question From the sample space, calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts., think step by step [/INST] These amounts are calculated by taking into account the different combinations of heads and tails that can occur when tossing a coin four times. The calculation for each amount is provided in the solution. , The answer is The different amounts of money that can be won are ₹ 4, ₹ 1.50, ₹ 1.50, ₹ 1.50, ₹ 1.50, -₹ 1, -₹ 1, -₹ 1, -₹ 1, -₹ 3.50, -₹ 3.50, -₹ 3.50, -₹ 3.50, -₹ 6.

[INST] help me answer this question Given, 2x – 3y > 6, think step by step [/INST] , The answer is The solution region of the given inequality is below the line 2x – 3y > 6. (Away from the origin.)

[INST] help me answer this question If the sum of the first p terms of an A.P. is equal to the sum of the first q terms, then find the sum of the first (p + q) terms., think step by step [/INST] Explanation provided in the markdown text outlines the steps to derive the answer. It includes the sum of p and q terms of the A.P. and their simplification leading to the relationship between p and q, and finally the sum of (p + q) terms. , The answer is The sum of (p + q) terms of the A.P. is 0.

[INST] help me answer this question Here, the vertices are on the x-axis, think step by step [/INST] , The answer is The vertices lie on the x-axis in the given problem.

[INST] help me answer this question , think step by step [/INST] , The answer is

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Calculate the mean deviation about the mean for the data: 5, 10, 15, 20, 25., think step by step [/INST] First, we find the mean of the data, then we calculate the absolute deviations from the mean, and finally, we find the mean of these deviations. , The answer is The mean deviation about the mean for the given data is 7.5.

[INST] help me answer this question Substitute the value of b² in equation (4), 1/a² = 1/16(1 – 9/b²)., think step by step [/INST] , The answer is a² = 52

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question There are two ways in which vowels and consonants can appear together: (AEIOU) (QTN) or (QTN) (AEIOU). How many total number of ways can vowel and consonant appear together?, think step by step [/INST] , The answer is The total number of ways in which vowel and consonant can appear together are 2 × 5C5 × 3C3 = 1440.

[INST] help me answer this question Find the derivative of the following functions. (i) sin x cos x, think step by step [/INST] , The answer is The derivative of sin x cos x is not provided.

[INST] help me answer this question For x + y ≤ 6, x + y ≥ 4, find the region of the solution., think step by step [/INST] , The answer is The region of the solution for the given inequalities is the area on the left side of the line x + y = 6, including the origin, and the area above the line x + y = 4 or the area on the right of the line.

[INST] help me answer this question What is the fourth inequality given in the problem?, think step by step [/INST] , The answer is x ≥ 0

[INST] help me answer this question Here, the elements of this set are natural numbers as well as divisors of 6. Hence, (i) matches with (c)., think step by step [/INST] , The answer is The elements of set (i) are natural numbers and divisors of 6, which makes it match with set (c).

[INST] help me answer this question Calculate the mean deviation about median age for the age distribution of 100 persons given below:, think step by step [/INST] The solution for this question involves calculating mean deviation about median age for the given age distribution. , The answer is None

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?, think step by step [/INST] Using the formula n(S ∪ T) = n(S) + n(T) - n(S ∩ T) , we find n(S ∪ T) = 42 , The answer is n(S ∪ T) = 42

[INST] help me answer this question Show that the statement p: “If x is a real number such that x^3 + 4x = 0, then x is 0” is true by (i) direct method, think step by step [/INST] In this method, we assume the given condition is true and using this assumption if we can prove the result then the statement is true. We assume q is true, which gives us x^3 + 4x = 0. Further, this results in x = 0 or x^2 + 4 = 0. Since x is real, x = 0, making statement r true. Thus, statement p is true. , The answer is The statement p is true by the direct method.

[INST] help me answer this question In which direction is the solution area for the first inequality?, think step by step [/INST] , The answer is The solution area for the first inequality is towards the origin, including the same.

[INST] help me answer this question F ∩ I, think step by step [/INST] I is not defined in the question. , The answer is F ∩ I = (3, 4, 5, 6) ∩ (I) = Not provided

[INST] help me answer this question Find the value of z in the following equation: 5(2z + 3) - 10 = 35, think step by step [/INST] To find the value of z, we first distribute the 5 to both terms inside the parentheses, which gives us 10z + 15 - 10 = 35. Then, we simplify the expression on the left side of the equation to get 10z + 5 = 35. Next, we subtract 5 from both sides to get 10z = 30. Finally, we divide both sides by 10 to get z = 3. , The answer is The value of z is 3.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question What is the value of the current if a charge of 6 coulombs passes through a point in 2 seconds?, think step by step [/INST] The value of current is given by the formula I = Q/t, where I is the current, Q is the charge, and t is the time. Substituting the given values, we get I = 6/2 = 3 amperes. , The answer is The value of the current is 3 amperes.

[INST] help me answer this question Is the square of every number an even number?, think step by step [/INST] The square of a number is an even number when the number is even, otherwise it's an odd number. , The answer is No.

[INST] help me answer this question False., think step by step [/INST] , The answer is Elements of {a, b, c} are a, b, c. Hence, {a} ⊂ {a, b, c}

[INST] help me answer this question Reduce the following equations into intercept form and find their intercepts on the axes. (i) 3x + 2y – 12 = 0 (ii) 4x – 3y = 6 (iii) 3y + 2 = 0, think step by step [/INST] The equation of a line in intercept form is x/a + y/b = 1, where a and b are the intercepts on the x and y axes, respectively. To reduce the given equations into intercept form, we need to rearrange them so that x and y are on the left-hand side and the constants are on the right-hand side. We then divide both sides by the constant term to get the intercepts. , The answer is Intercept on x-axis = 4, Intercept on y-axis = 6 Intercept on x-axis = 3/2, Intercept on y-axis = -2 Intercept on x-axis = 0, Intercept on y-axis = -2/3

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Find the equation of the median through the vertex R., think step by step [/INST] This is the equation of the median through the vertex R of the triangle. , The answer is 3x – 4y + 8 = 0

[INST] help me answer this question Find the equation of the parabola with equation x^2 = -16y., think step by step [/INST] On comparing the given equation with x^2 = -4ay, we get a = 4. The coordinates of the focus are (0,-a) = (0,-4). The given equation involves x^2, so the axis of the parabola is the y-axis. Therefore, the equation of directrix is y = a, which is y = 4. The length of latus rectum is 4a = 4(4) = 16. , The answer is x^2 = -16y.

[INST] help me answer this question What is the probability of getting at most two tails?, think step by step [/INST] , The answer is The probability of getting at most two tails is 7/8.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Find the variance for the data 4, 7., think step by step [/INST] The variance is calculated as the sum of (xi - x_mean)^2 divided by the number of observations, which comes out to be 2.25. , The answer is The variance of the data is 2.25.

[INST] help me answer this question Find the derivative of cos x from the first principle., think step by step [/INST] , The answer is The derivative of cos x from the first principle is not provided.

[INST] help me answer this question tan x = √3, think step by step [/INST] , The answer is The solution to this equation is not provided in the data.

[INST] help me answer this question Is 100 divisible by 5?, think step by step [/INST] A number is divisible by 5 if its units digit is either 0 or 5. The units digit of 100 is 0. Therefore, 100 is divisible by 5. , The answer is Yes, 100 is divisible by 5.

[INST] help me answer this question Factorize: 3x² - 11x - 4, think step by step [/INST] , The answer is 3x² - 11x - 4 = (3x + 1)(x - 4)

[INST] help me answer this question Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola x2/16 – y2/9 = 1, think step by step [/INST] Given the equation x2/16 – y2/9 = 1, we can compare it with the standard equation of a hyperbola x2/a2 – y2/b2 = 1. By doing so, we find that a = 4 and b = 3. We then calculate c using a2 + b2 = c2, which gives us c = 5. The coordinates of the foci are (±c, 0), so they are (±5, 0). The coordinates of the vertices are (±a, 0), so they are (±4, 0). The eccentricity is e = c/a = 5/4. The length of the latus rectum is given by 2b2/a = (2×9)/4 = 9/2. , The answer is The coordinates of the foci are (±5, 0), the coordinates of the vertices are (±4, 0), the eccentricity is e = c/a = 5/4, and the length of the latus rectum is 9/2.

[INST] help me answer this question Find the equation of the circle with Centre (1/2, 1/4) and radius (1/12)., think step by step [/INST] , The answer is 36x2 + 36y2 – 36x – 18y + 11= 0