Find an equation of the ellipse that satisfies the given conditions.
Foci: $( 0 , \pm 8 )$, vertices $( 0 , \pm 9 )$
A) $\frac { x ^ { 2 } } { 17 } + \frac { y ^ { 2 } } { 81 } = 1$
B) $\frac { x ^ { 2 } } { 17 } - \frac { y ^ { 2 } } { 81 } = 1$
C) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 17 } = 1$
D) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 17 } = 1$

Question

Quizplus · Accepted Answer

The foci are on the y-axis, so the major axis is vertical. The distance between the foci is 2c = 16, so c = 8. The distance between the vertices is 2a = 18, so a = 9. Therefore, the equation of the ellipse is $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, where $a^2 = 81$ and $b^2 = 17$. So, the equation of the ellipse is $\frac { x ^ { 2 } } { 17 } + \frac { y ^ { 2 } } { 81 } = 1$.

Find an Equation of the Ellipse That Satisfies the Given (0,±8)( 0 , \pm 8 )(0,±8)

Find an Equation of the Ellipse That Satisfies the Given $( 0 , \pm 8 )$