Find the standard form of the equation of the ellipse satisfying the given conditions.
-Major axis horizontal with length 20 ; length of minor axis $= 12 ;$ center $( 0,0 )$
A) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 144 } = 1$

Question

Quizplus · Accepted Answer

The standard form of an ellipse with a horizontal major axis 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. Given a major axis length of 20, $a = 10$, and a minor axis length of 12, $b = 6$. Thus, $a^2 = 100$ and $b^2 = 36$, leading to the equation $\frac{x^2}{100} + \frac{y^2}{36} = 1$.

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

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