options: (+)Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

Derive the equation of a parabola given a focus and directrix.

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
problem_activity: Problem 1
Write an equation that models each point’s distance from the center of the circle, point
$$A$$
.
[IMG]
Problem 2
A circle has a center at the origin and contains the point (
$$2, \space \sqrt{5}$$
).
Write an equation of the circle.
Identify the radius of this circle.
Name two other points that lie on this circle.


correct_option_index: 2