Find the standard form of the equation of the ellipse with the following characteristics.
foci: $( \pm 8,0 )$
major axis of length: 22
A) $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$
B) $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 64 } = 1$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 121 } = 1$
D) $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 64 } = 1$
E) $\frac { x ^ { 2 } } { 484 } + \frac { y ^ { 2 } } { 420 } = 1$

Question

Quizplus · Accepted Answer

The major axis is 22, so $2a = 22$, $a = 11$. The foci are $( \pm 8,0 )$, so $2c = 16$, $c = 8$. Therefore, $b^2 = a^2 - c^2 = 11^2 - 8^2 = 57$. The equation of the ellipse is $\frac { x ^ { 2 } } { a ^ { 2 } } + \frac { y ^ { 2 } } { b ^ { 2 } } = 1$, so the equation of this ellipse is $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 57 } = 1$.

Find the Standard Form of the Equation of the Ellipse (±8,0)( \pm 8,0 )(±8,0)

Find the Standard Form of the Equation of the Ellipse $( \pm 8,0 )$