Find an equation for the ellipse that has its center at the origin and satisfies the conditions. $\text { vertices } V ( \pm 7,0 ) \text {, foci } F ( \pm 3,0 )$
A) $\frac { x ^ { 2 } } { 58 } + \frac { y ^ { 2 } } { 40 } = 1$
B) $\frac { x ^ { 2 } } { 40 } + \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 40 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 58 } = 1$
E) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 40 } = 1$

Question

Quizplus · Accepted Answer

The standard form of an ellipse centered at the origin with horizontal major axis is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. Here, $a = 7$ (distance to vertices) and $c = 3$ (distance to foci). Using $c^2 = a^2 - b^2$, we find $b^2 = 49 - 9 = 40$. Thus, the equation is $\frac{x^2}{49} + \frac{y^2}{40} = 1$.

Find an Equation for the Ellipse That Has Its Center vertices V(±7,0), foci F(±3,0)\text { vertices } V ( \pm 7,0 ) \text {, foci } F ( \pm 3,0 ) vertices V(±7,0), foci F(±3,0)

Find an Equation for the Ellipse That Has Its Center $\text { vertices } V ( \pm 7,0 ) \text {, foci } F ( \pm 3,0 )$