Write an equation for the ellipse.
-eccentricity $\frac { 3 } { 5 }$; vertices at $( 0 , - 5 ) , ( 0,5 )$
A) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } = 1$
B) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 5 } = 1$
C) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } = 1$
D) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 25 } = 1$

Question

Quizplus · Accepted Answer

The vertices indicate a vertical ellipse centered at the origin with $a = 5$. The eccentricity $e = \frac{3}{5}$ gives $c = 3$. Using $c^2 = a^2 - b^2$, we find $b^2 = 16$. Thus, the equation is $\frac{x^2}{16} + \frac{y^2}{25} = 1$.

Write an Equation for the Ellipse 35\frac { 3 } { 5 }53​

Write an Equation for the Ellipse $\frac { 3 } { 5 }$