Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Foci: $( \pm 2,0 )$ ; major axis of length 18

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 77 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 2 } = 1$
C) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 77 } = 1$
D) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 4 } = 1$
E) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 77 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. 
Foci: $( \pm 2,0 )$ ; major axis of length 18

A) $\frac { x ^ { 2 } } { 4 } + \frac { y ^ { 2 } } { 77 } = 1$
B) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 2 } = 1$
C) $\frac { x ^ { 2 } } { 81 } - \frac { y ^ { 2 } } { 77 } = 1$
D) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 4 } = 1$
E) $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 77 } = 1$

Quizplus · Accepted Answer

The major axis is horizontal and has length 18, so $2a = 18$ and $a = 9$. The foci are at $( \pm 2,0 )$, so $c = 2$. The standard form of the equation of an ellipse with center at the origin and major axis horizontal is $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, where $b ^ { 2 } = a ^ { 2 } - c ^ { 2 }$. Substituting $a = 9$ and $c = 2$, we get $b ^ { 2 } = 9 ^ { 2 } - 2 ^ { 2 } = 77$. Therefore, the equation of the ellipse is $\frac { x ^ { 2 } } { 81 } + \frac { y ^ { 2 } } { 77 } = 1$.

Find the Standard Form of the Equation of the Ellipse (±2,0)( \pm 2,0 )(±2,0)

Find the Standard Form of the Equation of the Ellipse $( \pm 2,0 )$