Question

For the given ellipse with foci (8, 10+6√2), (8, 10 - 6√2) and endpoints of the major axis (8, 21), (8, -1), what is the correct equation?

a) (x - 8)^2 + ((y - 10)^2)/121 = 49
b) (x + 8)^2 + ((y + 10)^2)/121 = 49
c) (x - 8)^2 + ((y - 10)^2)/16 = 49
d) (x + 8)^2 + ((y + 10)^2)/16 = 49

Answer 1

The correct equation of the given ellipse is (x + 8)^2 + ((y + 10)^2)/121 = 49 (option b).

Step-by-step explanation:

The equation of the given ellipse is (x + 8)^2 + ((y + 10)^2)/121 = 49 (option b).

Step-by-step explanation:

To find the equation of the ellipse, we first need to determine the center and the lengths of the major and minor axes.

From the given coordinates of the foci, we can conclude that the center of the ellipse is the point (8, 10).

The length of the major axis is the distance between the endpoints (8, 21) and (8, -1), which is 21 - (-1) = 22.

The length of the minor axis is equal to twice the distance between the center and one of the foci. Given that the distance is 6√2, the length of the minor axis is 2 * 6√2 = 12√2.

Therefore, the equation of the ellipse is (x + 8)^2 + ((y + 10)^2)/121 = 49.