Find the equation of the ellipse satisfying the given conditions.
-(4, 0), (-4, 0), (0, 3), (0, -3)are the endpoints of the major and minor axes.
A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 8 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The endpoints of the major axis are (4, 0) and (-4, 0), so the length of the major axis is 8, and its semi-major axis length is 4, which means $a=4$. The endpoints of the minor axis are (0, 3) and (0, -3), so the length of the minor axis is 6, and its semi-minor axis length is 3, which means $b=3$. The standard form of the ellipse equation is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, so substituting $a=4$ and $b=3$ gives $\frac{x^2}{16} + \frac{y^2}{9} = 1$.

Find the Equation of the Ellipse Satisfying the Given Conditions x264+y236=1\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 164x2​+36y2​=1

Find the Equation of the Ellipse Satisfying the Given Conditions $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 36 } = 1$