Find the standard form of the equation of the ellipse with the following characteristics.
Foci: $( \pm 3,0 )$ ,major axis of length: 16

A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$
B) $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$
E) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$

Question

Find the standard form of the equation of the ellipse with the following characteristics. ​
Foci: $( \pm 3,0 )$ ,major axis of length: 16
​
A) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 55 } = 1$
B) $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 247 } = 1$
C) $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 9 } = 1$
D) $\frac { x ^ { 2 } } { 256 } + \frac { y ^ { 2 } } { 9 } = 1$
E) $\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 64 } = 1$

Quizplus · Accepted Answer

The major axis is horizontal, so the equation is of the form $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$. The distance between the foci is 2c, so $2c=6$, or $c=3$. The length of the major axis is 2a, so $2a=16$, or $a=8$. Therefore, $b^2=a^2-c^2=8^2-3^2=55$. The equation of the ellipse is $\frac{x^2}{64}+\frac{y^2}{55}=1$.

Find the Standard Form of the Equation of the Ellipse (±3,0)( \pm 3,0 )(±3,0)

Find the Standard Form of the Equation of the Ellipse $( \pm 3,0 )$