Write the standard form of an equation of the ellipse subject to the given conditions.
-Foci: $( - 5,5 )$ and $( 3,5 )$
Length of minor axis: 4
A) $\frac { ( x + 1 ) ^ { 2 } } { 20 } + \frac { ( y - 5 ) ^ { 2 } } { 4 } = 1$
B) $\frac { ( x + 1 ) ^ { 2 } } { 4 } + \frac { ( y - 5 ) ^ { 2 } } { 20 } = 1$
C) $\frac { ( x - 5 ) ^ { 2 } } { 4 } + \frac { ( y + 1 ) ^ { 2 } } { 20 } = 1$
D) $\frac { ( x - 5 ) ^ { 2 } } { 20 } + \frac { ( y + 1 ) ^ { 2 } } { 4 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of the foci, which is $(\frac{-5+3}{2}, \frac{5+5}{2}) = (-1, 5)$. The distance between the foci is $3 - (-5) = 8$, so the distance from the center to a focus (c) is $4$. The length of the minor axis is 4, so the semi-minor axis (b) is $2$. Using $c^2 = a^2 - b^2$, we find $a^2 = c^2 + b^2 = 16 + 4 = 20$. Since the foci and center have the same y-coordinate, the major axis is horizontal, making the equation $\frac{(x+1)^2}{20} + \frac{(y-5)^2}{4} = 1$.

Write the Standard Form of an Equation of the Ellipse (−5,5)( - 5,5 )(−5,5)

Write the Standard Form of an Equation of the Ellipse $( - 5,5 )$