Question

An ellipse has a center at the origin, a vertex along the major axis at (0, 17), and a focus at (0, −8).

Which equation represents this ellipse?

Answer choices below vvv

Answer 1

D

Explanation:

egde 2020

Answer 2

The last one.

Explanation:

The standard form equation of an ellipse with foci on the y-axis is ...

y²/a² +x²/b² = 1

where "a" and "b" are the lengths of the semi-major and semi-minor axes, respectively. If "c" is the distance from the center to the focus, then this relation also holds:

b² +c² = a²

For this ellipse ...

b² + 8² = 17²

289 -64 = b² = 225 . . . . . subtract 8²

b = 15 . . . . . . . . . . . . . . . . . take the square root

The equation of the ellipse is then ...

y²/17² +x²/15² = 1