Find an equation for the ellipse described.
-Center at $( 0,0 ) ;$ focus at $( 0,5 )$; vertex at $( 0 , - 7 )$
A) $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$

C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$

D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$

Question

Find an equation for the ellipse described.
-Center at $( 0,0 ) ;$ focus at $( 0,5 )$; vertex at $( 0 , - 7 )$
A) $\frac { x ^ { 2 } } { 24 } + \frac { y ^ { 2 } } { 49 } = 1$

B) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 24 } = 1$

C) $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 49 } = 1$

D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 24 } = 1$

Quizplus · Accepted Answer

The distance between the center and the focus is 5, and the distance between the center and the vertex is 7. So, $c = 5$ and $a = 7$. Therefore, $b^2 = a^2 - c^2 = 49 - 25 = 24$. So, the equation of the ellipse is $\frac{x^2}{25} + \frac{y^2}{24} = 1$.

Find an Equation for the Ellipse Described (0,0);( 0,0 ) ;(0,0);

Find an Equation for the Ellipse Described $( 0,0 ) ;$