Write the standard form of an equation of the ellipse subject to the given conditions.
-Vertices: $( 0,10 )$ and $( 0 , - 10 )$
Passes through $\left( - \frac { 32 } { 5 } , 6 \right)$
A) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 100 } = 1$
B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$

Question

Quizplus · Accepted Answer

The vertices at $(0,10)$ and $(0,-10)$ indicate that the major axis is vertical, so the major radius $a=10$, and $a^2=100$. Since the ellipse passes through $\left(-\frac{32}{5}, 6\right)$, we use this point to find $b^2$. Plugging $x=-\frac{32}{5}$ and $y=6$ into the standard form of the ellipse equation, we solve for $b^2$, which gives us $b^2=64$. Therefore, the correct equation is $\frac{x^2}{64} + \frac{y^2}{100} = 1$.

Write the Standard Form of an Equation of the Ellipse (0,10)( 0,10 )(0,10)

Write the Standard Form of an Equation of the Ellipse $( 0,10 )$