Find an equation in standard form for the ellipse that satisfies the given conditions.
-An ellipse with foci at $( 2,0 )$ and $( 2 , - 6 )$; major axis length of 10
A) $\frac { ( y + 3 ) ^ { 2 } } { 25 } + \frac { ( x - 2 ) ^ { 2 } } { 16 } = 1$
B) $\frac { ( y + 3 ) ^ { 2 } } { 25 } + \frac { ( x + 2 ) ^ { 2 } } { 16 } = 1$
C) $\frac { ( x + 3 ) ^ { 2 } } { 16 } + \frac { ( y + 2 ) ^ { 2 } } { 25 } = 1$
D) $\frac { ( x + 3 ) ^ { 2 } } { 25 } + \frac { ( y + 2 ) ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The foci are vertically aligned, indicating the major axis is vertical. The distance between the foci is 6, so $c=3$. The major axis length is 10, so $a=5$. The center is midway between the foci at $(2,-3)$. Using $a^2=25$ and $c^2=9$, we find $b^2=a^2-c^2=16$. The correct equation is $\frac{(y+3)^2}{25}+\frac{(x-2)^2}{16}=1$.

Find an Equation in Standard Form for the Ellipse That (2,0)( 2,0 )(2,0)

Find an Equation in Standard Form for the Ellipse That $( 2,0 )$