Find an equation in standard form for the ellipse that satisfies the given conditions.
-An ellipse with major axis from $( - 2 , - 2 )$ to $( 10 , - 2 )$; minor axis from $( 4 , - 4 )$ to $( 4,0 )$
A) $\frac { ( x - 4 ) ^ { 2 } } { 36 } + \frac { ( y + 2 ) ^ { 2 } } { 4 } = 1$
B) $\frac { ( x - 6 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$
C) $\frac { ( x + 2 ) ^ { 2 } } { 36 } + \frac { ( y - 4 ) ^ { 2 } } { 4 } = 1$
D) $\frac { ( x + 4 ) ^ { 2 } } { 36 } + \frac { ( y - 2 ) ^ { 2 } } { 4 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of the major axis, which is $(\frac{-2+10}{2}, \frac{-2-2}{2}) = (4, -2)$. The length of the major axis is 12 (from -2 to 10), so $a=6$ and $a^2=36$. The length of the minor axis is 4 (from -4 to 0), so $b=2$ and $b^2=4$. The standard form of the ellipse is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center. Substituting the values, we get $\frac{(x-4)^2}{36} + \frac{(y+2)^2}{4} = 1$.

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

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