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 equation of an ellipse with foci along the y-axis is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis, $2b$ is the length of the minor axis, and $c$ is the distance from the center to a focus. Here, $b^2 = a^2 - c^2$. Given vertices $(0, \pm9)$ indicate $a = 9$, and foci $(0, \pm8)$ indicate $c = 8$. Solving for $b^2$, we get $b^2 = 9^2 - 8^2 = 81 - 64 = 17$. Thus, the correct equation 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 $( 0 , \pm 8 )$