Find an equation for the ellipse described.
-Center at (0, 0); focus at (-2, 0); vertex at (3, 0)
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Find an equation for the ellipse described.
-Center at (0, 0); focus at (-2, 0); vertex at (3, 0) 
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 9 } = 1$

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. The distance from the center to a vertex (a) is 3, so $a^2 = 9$. The distance from the center to a focus (c) is 2, and $c^2 = a^2 - b^2$. Solving for $b^2$ gives $b^2 = a^2 - c^2 = 9 - 4 = 5$. Therefore, the correct equation is $\frac{x^2}{9} + \frac{y^2}{5} = 1$.

Find an Equation for the Ellipse Described x29+y25=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 19x2​+5y2​=1

Find an Equation for the Ellipse Described $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$