Find an equation for the ellipse described.
-Foci at $( \pm 2,0 ) ; \quad x$-intercepts are $\pm 7$
A) $\frac { x ^ { 2 } } { 45 } + \frac { y ^ { 2 } } { 49 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 45 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$

Question

Quizplus · Accepted Answer

The ellipse has foci at $( \pm 2,0 )$ and x-intercepts at $\pm 7$, indicating a horizontal major axis. The equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with $a = 7$ and $c = 2$. Using $c^2 = a^2 - b^2$, we find $b^2 = 45$. Thus, the equation is $\frac{x^2}{49} + \frac{y^2}{45} = 1$.

Find an Equation for the Ellipse Described (±2,0);x( \pm 2,0 ) ; \quad x(±2,0);x

Find an Equation for the Ellipse Described $( \pm 2,0 ) ; \quad x$