Write an equation for the ellipse.
-foci at $( \pm 4 \sqrt { 2 } , 0 ) ; x$-intercepts $( \pm 9,0 )$
A) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 49 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 7 } = 1$
C) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = 1$

Question

Quizplus · Accepted Answer

The equation of an ellipse with foci on the x-axis is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis, $2b$ is the length of the minor axis, and $c$ is the distance from the center to a focus. Given the foci at $(\pm 4\sqrt{2}, 0)$, we have $c = 4\sqrt{2}$. The x-intercepts at $(\pm 9,0)$ indicate that $a = 9$, so $a^2 = 81$. Using the relationship $c^2 = a^2 - b^2$, we find $b^2 = a^2 - c^2 = 81 - (4\sqrt{2})^2 = 81 - 32 = 49$. Therefore, the correct equation is $\frac{x^2}{81} + \frac{y^2}{49} = 1$.

Write an Equation for the Ellipse (±42,0);x( \pm 4 \sqrt { 2 } , 0 ) ; x(±42​,0);x

Write an Equation for the Ellipse $( \pm 4 \sqrt { 2 } , 0 ) ; x$