Write an equation for the ellipse.
-foci at $( \pm 2 \sqrt { 10 } , 0 ) ; x$-intercepts $( \pm 7,0 )$
A) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 3 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 7 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 9 } = 1$

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 $c = 2\sqrt{10}$ and the x-intercepts ($\pm 7,0$) indicating $a = 7$, we find $b^2 = a^2 - c^2 = 49 - 40 = 9$, leading to the equation $\frac{x^2}{49} + \frac{y^2}{9} = 1$.

Write an Equation for the Ellipse (±210,0);x( \pm 2 \sqrt { 10 } , 0 ) ; x(±210​,0);x

Write an Equation for the Ellipse $( \pm 2 \sqrt { 10 } , 0 ) ; x$