Find the standard form of the equation of the ellipse satisfying the given conditions.
-Major axis horizontal with length 20; length of minor axis = 16; center (0, 0)
A) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$
B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 256 } = 1$

Question

Find the standard form of the equation of the ellipse satisfying the given conditions.
-Major axis horizontal with length 20; length of minor axis = 16; center (0, 0) 
A) $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$
B) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 100 } = 1$
C) $\frac { x ^ { 2 } } { 20 } + \frac { y ^ { 2 } } { 64 } = 1$
D) $\frac { x ^ { 2 } } { 400 } + \frac { y ^ { 2 } } { 256 } = 1$

Quizplus · Accepted Answer

The standard form of the equation 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, $a = 10$, so $a^2 = 100$. Given a minor axis length of 16, $b = 8$, so $b^2 = 64$. Therefore, the correct equation is $\frac{x^2}{100} + \frac{y^2}{64} = 1$.

Find the Standard Form of the Equation of the Ellipse x2100+y264=1\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1100x2​+64y2​=1

Find the Standard Form of the Equation of the Ellipse $\frac { x ^ { 2 } } { 100 } + \frac { y ^ { 2 } } { 64 } = 1$