Write the standard form of an equation of the ellipse subject to the given conditions.
-Endpoints of minor axis: $( \sqrt { 31 } , 0 )$ and $( - \sqrt { 31 } , 0 )$
Foci: $( 0,10 )$ and $( 0 , - 10 )$
A) $\frac { x ^ { 2 } } { 41 } + \frac { y ^ { 2 } } { 31 } = 1$
B) $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 41 } = 1$
C) $\frac { x ^ { 2 } } { 31 } + \frac { y ^ { 2 } } { 131 } = 1$
D) $\frac { x ^ { 2 } } { 131 } + \frac { y ^ { 2 } } { 31 } = 1$

Question

Quizplus · Accepted Answer

The endpoints of the minor axis indicate that the length of the minor axis is $2\sqrt{31}$, so $b^2 = 31$. The foci indicate that the distance from the center to each focus is 10, so $c = 10$. Using the relationship $c^2 = a^2 - b^2$, we find $a^2 = 131$. Thus, the equation is $\frac{x^2}{31} + \frac{y^2}{131} = 1$.

Write the Standard Form of an Equation of the Ellipse (31,0)( \sqrt { 31 } , 0 )(31​,0)

Write the Standard Form of an Equation of the Ellipse $( \sqrt { 31 } , 0 )$