Find an equation in standard form for the ellipse that satisfies the given conditions.
-The horizontal major axis is of length 18 , and the minor axis is of length 10 .
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $\frac { x ^ { 2 } } { 5 } + \frac { y ^ { 2 } } { 9 } = 1$

Question

Quizplus · Accepted Answer

The lengths of the major and minor axes are 18 and 10, respectively. 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. Here, $2a = 18$ so $a = 9$, and $2b = 10$ so $b = 5$. Therefore, $a^2 = 81$ and $b^2 = 25$, making the correct equation $\frac{x^2}{81} + \frac{y^2}{25} = 1$.

Find an Equation in Standard Form for the Ellipse That x225+y281=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 125x2​+81y2​=1

Find an Equation in Standard Form for the Ellipse That $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 81 } = 1$