Write the standard form of an equation of the ellipse subject to the given conditions.
-Center $( 0,0 )$; Eccentricity: $\frac { 24 } { 25 }$; Major axis vertical of length 50 units
A) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 625 } = 1$
B) $\frac { x ^ { 2 } } { 576 } + \frac { y ^ { 2 } } { 625 } = 1$
C) $\frac { x ^ { 2 } } { 625 } + \frac { y ^ { 2 } } { 49 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 576 } = 1$

Question

Quizplus · Accepted Answer

The major axis is vertical, so the equation is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$. The length of the major axis is 50, so $a = 25$ and $a^2 = 625$. The eccentricity $e = \frac{24}{25}$, so $c = ae = 24$ and $c^2 = 576$. Using $c^2 = a^2 - b^2$, we find $b^2 = 49$. Thus, the equation is $\frac{x^2}{49} + \frac{y^2}{625} = 1$.

Write the Standard Form of an Equation of the Ellipse (0,0)( 0,0 )(0,0)

Write the Standard Form of an Equation of the Ellipse $( 0,0 )$