Question

Which of the following statements is a fact about​ ellipses?

Choose the correct statement below.
A.
The square of the length of the major axis is equal to the difference between the square of the length of the minor axis and the square of the distance from the center of the ellipse to a focus.
B.
The sum of the squares of the distances between the two foci and the center is equal to the square of the length of the minor axis.
C.
The square of half the length of the minor axis is equal to the difference between the square of half the length of the major axis and the square of the distance from the center of the ellipse to a focus.
D.
The sum of the squares of the distances between the two foci and a fixed point on the ellipse is equal to the square of the length of the major axis.

Answer 1

c is the correct choice

because it's true

Answer 2

C

Explanation:

The distance from the focus to the co-vertex is the length of the semi-major axis. Expressed in terms of the Pythagorean theorem, that relationship matches the description in selection C:

• The square of the semi-minor axis is equal the the difference between the square of the semi-major axis and the square of the distance from the center to a focus.