Write the standard form of the equation of the ellipse centered at the origin. Vertices: $( - 6,0 ) ( 6,0 )$ Co-vertices: $( 0 , - 4 ) , ( 0,4 )$
A) $\frac { x ^ { 2 } } { 6 } = \frac { y ^ { 2 } } { 4 }$
B) $36 x ^ { 2 } + 16 y ^ { 2 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 6 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 0$
E) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The standard form of the equation of an ellipse centered at the origin is $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, where $a$ is the distance from the center to the vertices, and $b$ is the distance from the center to the co-vertices. In this case, we have $a=6$ and $b=4$, so the equation is $\frac{x^2}{36}+\frac{y^2}{16}=1$, which is equivalent to choice E.

Write the Standard Form of the Equation of the Ellipse (−6,0)(6,0)( - 6,0 ) ( 6,0 )(−6,0)(6,0)

Write the Standard Form of the Equation of the Ellipse $( - 6,0 ) ( 6,0 )$