Find an equation of the ellipse that satisfies the given conditions. Foci: (0, ± 8), vertices (0, ± 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 ellipse is vertical with center at (0,0), vertices at (0,±9), so a=9. The distance from the center to the foci is c=8. Using c^2 = a^2 - b^2, we find b^2 = 81 - 64 = 17. Thus, the equation is $\frac{x^2}{17} + \frac{y^2}{81} = 1$.

Find an Equation of the Ellipse That Satisfies the Given x217+y281=1\frac { x ^ { 2 } } { 17 } + \frac { y ^ { 2 } } { 81 } = 117x2​+81y2​=1

Find an Equation of the Ellipse That Satisfies the Given $\frac { x ^ { 2 } } { 17 } + \frac { y ^ { 2 } } { 81 } = 1$