Find the standard form of the equation of the ellipse with the following characteristics.
foci: $( \pm 4,0 ) \quad$ major axis of length: 14
A) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$
B) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 16 } = 1$
C) $\frac { x ^ { 2 } } { 16 } + \frac { y ^ { 2 } } { 49 } = 1$
D) $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 16 } = 1$
E) $\frac { x ^ { 2 } } { 196 } + \frac { y ^ { 2 } } { 180 } = 1$

Question

Quizplus · Accepted Answer

The major axis is horizontal, and the length of the major axis is 14, so $2a = 14$, and $a = 7$. The foci are at $( \pm 4,0 ) $, so $c = 4$. Using the relationship $c^2 = a^2 - b^2$, we have $4^2 = 7^2 - b^2$, so $b^2 = 33$. Therefore, the equation of the ellipse is $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$.

Find the Standard Form of the Equation of the Ellipse (±4,0)( \pm 4,0 ) \quad(±4,0)

Find the Standard Form of the Equation of the Ellipse $( \pm 4,0 ) \quad$