Find the standard form of the equation of the ellipse satisfying the given conditions.
-Major axis vertical with length $12 ;$ length of minor axis $= 6 ;$ center $( 0,0 )$
A) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 144 } = 1$

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 $2a = 12$ and $2b = 6$, we find $a = 6$ and $b = 3$. Thus, $a^2 = 36$ and $b^2 = 9$, leading to the equation $\frac{x^2}{9} + \frac{y^2}{36} = 1$.

Find the Standard Form of the Equation of the Ellipse 12;12 ;12;

Find the Standard Form of the Equation of the Ellipse $12 ;$