Write the standard form of the equation of the ellipse.
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$
B) $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$
D) $25 x ^ { 2 } + 9 y ^ { 2 } = 1$
E) $\frac { 9 x ^ { 2 } } { 25 } + \frac { 25 y ^ { 2 } } { 9 } = 1$

Question

Write the standard form of the equation of the ellipse. 
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$ 
B) $\frac { x ^ { 2 } } { 3 } + \frac { y ^ { 2 } } { 5 } = 1$ 
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 25 } = 1$ 
D) $25 x ^ { 2 } + 9 y ^ { 2 } = 1$ 
E) $\frac { 9 x ^ { 2 } } { 25 } + \frac { 25 y ^ { 2 } } { 9 } = 1$

Quizplus · Accepted Answer

The standard form of the equation of the ellipse is $\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1$ where $(h,k)$ is the center of the ellipse and $a$ and $b$ are the lengths of the semi-major and semi-minor axes, respectively. Comparing this to the given equation $\frac{x^2}{9}+\frac{y^2}{25}=1$, we see that $h = 0$, $k = 0$, $a = 3$, and $b = 5$. Therefore, the standard form of the equation of the ellipse is $\frac{x^2}{3^2}+\frac{y^2}{5^2}=1$, which corresponds to choice C).

Write the Standard Form of the Equation of the Ellipse x225+y29=1\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 125x2​+9y2​=1

Write the Standard Form of the Equation of the Ellipse $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 9 } = 1$