Find the standard form of the equation of the ellipse satisfying the given conditions.
-Endpoints of major axis: $( - 7,4 )$ and $( 9,4 )$; endpoints of minor axis: $( 1 , - 1 )$ and $( 1,9 )$
A) $\frac { ( x - 1 ) ^ { 2 } } { 64 } + \frac { ( y - 4 ) ^ { 2 } } { 25 } = 1$
B) $\frac { ( x - 4 ) ^ { 2 } } { 25 } + \frac { ( y - 1 ) ^ { 2 } } { 64 } = 1$
C) $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 0$
D) $\frac { ( x + 1 ) ^ { 2 } } { 64 } + \frac { ( y - 5 ) ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The center of the ellipse is the midpoint of both the major and minor axes, which is $(1, 4)$. The length of the major axis is $16$ (from $-7$ to $9$), so $a = 8$ and $a^2 = 64$. The length of the minor axis is $10$ (from $-1$ to $9$), so $b = 5$ and $b^2 = 25$. The major axis is horizontal, so the equation is $\frac{(x-1)^2}{64} + \frac{(y-4)^2}{25} = 1$.

Find the Standard Form of the Equation of the Ellipse (−7,4)( - 7,4 )(−7,4)

Find the Standard Form of the Equation of the Ellipse $( - 7,4 )$