Find an equation for the ellipse described.
-Center (0, 0); major axis vertical with length 12; length of minor axis is 8
A) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 144 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$

Question

Find an equation for the ellipse described.
-Center (0, 0); major axis vertical with length 12; length of minor axis is 8 
A) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 144 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 36 } = 1$

Quizplus · Accepted Answer

The equation of an ellipse with center at (0,0) 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. Since the major axis is vertical, $2a = 12$ and $2b = 8$, giving $a = 6$ and $b = 4$. Therefore, $a^2 = 36$ and $b^2 = 16$, leading to the equation $\frac{x^2}{16} + \frac{y^2}{36} = 1$.

Find an Equation for the Ellipse Described x28+y236=1\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 36 } = 18x2​+36y2​=1

Find an Equation for the Ellipse Described $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 36 } = 1$