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

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) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 45 } = 1$

Quizplus · Accepted Answer

The ellipse has foci at $( \pm 2,0 )$, so $c = 2$. The x-intercepts are $\pm 7$, so $a = 7$. The relationship $c^2 = a^2 - b^2$ gives $4 = 49 - b^2$, so $b^2 = 45$. 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 $( \pm 2,0 ) ; \quad x$