Find an equation for the ellipse described.
-Foci at (0, -3)and (0, 3); length of the major axis is 12
A) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 1$
B) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 6 } = 1$
C) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 6 } = 1$
D) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$

Question

Find an equation for the ellipse described.
-Foci at (0, -3)and (0, 3); length of the major axis is 12 
A) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 1$
B) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 6 } = 1$
C) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 6 } = 1$
D) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$

Quizplus · Accepted Answer

The foci are on the y-axis, so the major axis is vertical. The center is at (0,0), and the length of the major axis is 12, so $2a = 12$ giving $a = 6$. The distance from the center to each focus is $c = 3$. Using $b^2 = a^2 - c^2$, we find $b^2 = 36 - 9 = 27$. The equation is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, which is $\frac{x^2}{27} + \frac{y^2}{36} = 1$.

Find an Equation for the Ellipse Described x236+y227=1\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 136x2​+27y2​=1

Find an Equation for the Ellipse Described $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 27 } = 1$