Find the standard form of the equation of the ellipse with the given characteristics and center at the origin.
Vertices: (0,±7);focies: (0,±4)

A) $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$$
B) $$\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$$
C) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = - 1$
D) $- \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$
E) $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = - 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. ​
Vertices: (0,±7);focies: (0,±4)
​
A) $$\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$$
B) $$\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = 1$$
C) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = - 1$
D) $- \frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$
E) $\frac { x ^ { 2 } } { 33 } + \frac { y ^ { 2 } } { 49 } = - 1$

Quizplus · Accepted Answer

The standard form of the equation of an ellipse with center at the origin is $\frac { x ^ { 2 } } { b ^ { 2 } } + \frac { y ^ { 2 } } { a ^ { 2 } } = 1$. The vertices are on the y-axis, so $a=7$. The foci are on the y-axis, so $c=4$. Using the relationship $c^2=a^2-b^2$, we can find that $b^2=33$. 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 x249+y233=1\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 149x2​+33y2​=1

Find the Standard Form of the Equation of the Ellipse $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 33 } = 1$