Find an equation in standard form for the ellipse that satisfies the given conditions.
-The vertical major axis is of length 8 , and the minor axis is of length 4 .
A) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$
B) $\frac { x ^ { 2 } } { 2 } + \frac { y ^ { 2 } } { 4 } = 1$
C) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 2 } = 1$
D) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 16 } = 1$

Question

Quizplus · Accepted Answer

The standard form of an ellipse with a vertical major axis is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. Given that the major axis is 8 and the minor axis is 4, we have $2a = 8$ (so $a = 4$) and $2b = 4$ (so $b = 2$). Therefore, $a^2 = 16$ and $b^2 = 4$, and the correct equation is $\frac{x^2}{4} + \frac{y^2}{16} = 1$.

Find an Equation in Standard Form for the Ellipse That x216+y24=1\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 116x2​+4y2​=1

Find an Equation in Standard Form for the Ellipse That $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 4 } = 1$