Write an equation for the ellipse.
-$x$-intercepts $( \pm 2,0 ) ; y$-intercepts $( 0 , \pm 8 )$
A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 64 } = 1$
C) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 2 } = 1$
D) $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 8 } = 1$

Question

Quizplus · Accepted Answer

The general equation for an ellipse is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. The $x$-intercepts at $(\pm 2,0)$ indicate that $a = 2$, so $a^2 = 4$. The $y$-intercepts at $(0, \pm 8)$ indicate that $b = 8$, so $b^2 = 64$. Therefore, the correct equation is $\frac{x^2}{4} + \frac{y^2}{64} = 1$.

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