Question

guided practice
if c=8, find the coordinates of c and c.
a. (0, 8) and (0, -8)
b. (0, 64) and (0, -64)
c. (64, 0) and (-64, 0)
d. (8, 0) and (-8, 0)
image of an ellipse with center at the origin, major axis along the y-axis, and a dashed line of length 10 from a point on the ellipse to the top vertex

Explanation:

Step1: Identify ellipse parameters

From the graph, the distance from vertex B to focus C' is 10, so $a=10$. We know $c=8$.

Step2: Confirm focus axis

The ellipse has vertices on the x-axis, so foci lie on the x-axis, with coordinates $(\pm c, 0)$.

Step3: Substitute c value

Substitute $c=8$: Coordinates are $(8,0)$ and $(-8,0)$.

Answer:

D. (8, 0) and (-8, 0)