Find an equation in standard form for the ellipse that satisfies the given conditions.
-An ellipse with center at origin, length of major axis 14 and $y$-intercepts $( 0 , \pm 6 )$
A) $\frac { x ^ { 2 } } { 6 } + \frac { y ^ { 2 } } { 7 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { y ^ { 2 } } { 49 } = 1$
C) $\frac { x ^ { 2 } } { 7 } + \frac { y ^ { 2 } } { 6 } = 1$
D) $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 36 } = 1$

Question

Quizplus · Accepted Answer

The standard form of an ellipse centered at the origin is $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. Given the length of the major axis is 14, $a = 7$, and the $y$-intercepts are $\pm 6$, indicating $b = 6$. Thus, the correct equation is $\frac{x^2}{49} + \frac{y^2}{36} = 1$.

Find an Equation in Standard Form for the Ellipse That yyy

Find an Equation in Standard Form for the Ellipse That $y$