Find an equation in standard form for the ellipse that satisfies the given conditions.
-Major axis endpoints $( 0 , \pm 9 )$, minor axis length 10
A) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { y ^ { 2 } } { 81 } + \frac { x ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$

Question

Quizplus · Accepted Answer

The major axis endpoints $(0, \pm 9)$ indicate that the major axis is vertical, so $a = 9$ and $a^2 = 81$. The minor axis length is 10, so $b = 5$ and $b^2 = 25$. Therefore, the correct equation is $\frac{y^2}{81} + \frac{x^2}{25} = 1$, which matches option C.

Find an Equation in Standard Form for the Ellipse That (0,±9)( 0 , \pm 9 )(0,±9)

Find an Equation in Standard Form for the Ellipse That $( 0 , \pm 9 )$