Find an equation for the ellipse described.
-Focus at $( - 3,0 )$; vertices at $( \pm 5,0 )$
A) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The vertices at $(\pm 5,0)$ indicate that the major axis is along the x-axis, and the length of the major axis is $2a = 10$, so $a = 5$ and $a^2 = 25$. The focus at $(-3,0)$ suggests that the ellipse is centered at the origin and the distance from the center to a focus, $c$, is 3, so $c^2 = 9$. The relationship between $a$, $b$, and $c$ in an ellipse is $a^2 = b^2 + c^2$. Solving for $b^2$, we get $b^2 = a^2 - c^2 = 25 - 9 = 16$. Therefore, the equation of the ellipse is $\frac{x^2}{25} + \frac{y^2}{16} = 1$.

Find an Equation for the Ellipse Described (−3,0)( - 3,0 )(−3,0)

Find an Equation for the Ellipse Described $( - 3,0 )$