Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( 5,0 )$; vertex at $( 7,0 )$

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

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

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

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

Question

Find an equation for the ellipse described.
-Center at $( 0,0 )$; focus at $( 5,0 )$; vertex at $( 7,0 )$

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

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

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

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

Quizplus · Accepted Answer

The equation of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis, $2b$ is the length of the minor axis, and $c$ is the distance from the center to a focus. Here, $a = 7$ (since the vertex is at $(7,0)$), and $c = 5$ (since the focus is at $(5,0)$). We find $b^2 = a^2 - c^2 = 49 - 25 = 24$, so the equation is $\frac{x^2}{49} + \frac{y^2}{24} = 1$.

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

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