Assertion: parabola's distance | /r/HasProperty | equal
Facets:
value: always
type: DEGREE
value: to a fixed point
type: OTHER
value: for a point
type: PURPOSE
value: to the distance from p
type: OTHER
Source sentences:
text: The distances EF and EC are equal because E is on the parabola, F is the focus and C is on the directrix.
text: As a plane curve, it may be defined as the path (locus) of a point moving so that its distance from a fixed line (the directrix) is equal to its distance from a fixed point (the focus).
text: Finally, notice that the distance from the focus to the vertex is equal to the distance from the vertex to the directrix.
text: Therefore, let us find all points P(x,y) such that FG and the distance from G to the line are equal.
text: The name "parabola" is derived from a New Latin term that means something similar to "compare" or "balance", and refers to the fact that the distance from the parabola to the focus is always equal to (that is, is always in balance with) the distance from the parabola to the directrix.
text: For a parabola, the ratio is 1, so the two distances are equal .
text: This website: https://www.intmath.com/plane-analytic-geometry/parabola-interactive.php Is also very helpful in showing the relationships between the focus, directrix and the graph of the parabolas because students can clearly see that the distance between a point on the parabola and the focus and the distance between that same point and the directrix are equal.
text: A parabola is defined as a collection of points such that the distance to a fixed point (the focus) and a fixed straight line (the directrix) are equal.
text: And since the distances of two of the sides are equal, they are isosceles triangles.
text: According to the above definition of the parabola these two distances are equal; hence
text: A parabola is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to the distance from a fixed straight line in the same plane.
text: Since by definition these two distances are equal, we may set them equal: Squaring both sides, we have Figure 2-8.-The parabola.
text: A common definition defines it as the locus of points P such that the distance from a line (called the directrix) to P is equal to the distance from P to a fixed point F (called the focus).
text: Therefore for a point to be on a parabola, the distance from the point to the focus must be equal to the distance from the point to the directrix.
text: That a parabola is indeed generated can be seen from the focus-directrix definition, since the distance of the pencil from the focus will always be equal to the distance of the pencil directly above the directrix.
text: A parabola is the locus of a point which moves in a plane such that its distance from a fixed point in the plane is always equal to its distance from a fixed straight line in the same plane.
text: These distances must be equal for a parabola to be a parabola; it defines a parabola.