Find an equation in standard form for the ellipse that satisfies the given conditions.
-An ellipse with intercepts $( \pm 5,0 )$ and $( 0 , \pm 6 )$, center at origin
A) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 5 } = 1$
B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 36 } = 1$
C) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 6 } = 1$

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 $2a$ and $2b$ are the lengths of the major and minor axes, respectively. The given intercepts $(\pm 5,0)$ and $(0, \pm 6)$ indicate that $a=5$ and $b=6$, so the equation becomes $\frac{x^2}{25} + \frac{y^2}{36} = 1$.

Find an Equation in Standard Form for the Ellipse That (±5,0)( \pm 5,0 )(±5,0)

Find an Equation in Standard Form for the Ellipse That $( \pm 5,0 )$