Find the standard-form equation of the ellipse centered at the origin and satisfying the given conditions.
-An ellipse with length of major axis 18 and $y$-intercepts $( 0 , \pm 5 )$
A) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 1$
D) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The standard form 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. Given the length of the major axis is 18, $a = 9$, so $a^2 = 81$. The $y$-intercepts $(0, \pm 5)$ indicate that the minor axis length is 10, so $b = 5$ and $b^2 = 25$. Therefore, the correct equation is $\frac{x^2}{81} + \frac{y^2}{25} = 1$.

Find the Standard-Form Equation of the Ellipse Centered at the Origin