Write an equation for the ellipse.
-foci at $( 0,11 ) , ( 0 , - 11 )$, through the point $\left( 1 , \frac { 61 \sqrt { 3599 } } { 60 } \right)$
A) $\frac { x ^ { 2 } } { 61 } + \frac { y ^ { 2 } } { 60 } = 1$
B) $\frac { x ^ { 2 } } { 60 } + \frac { y ^ { 2 } } { 61 } = 1$
C) $\frac { x ^ { 2 } } { 3600 } + \frac { y ^ { 2 } } { 3721 } = 1$
D) $\frac { x ^ { 2 } } { 3721 } + \frac { y ^ { 2 } } { 3600 } = 1$

Question

Quizplus · Accepted Answer

The foci indicate a vertical ellipse with center at the origin. The distance from the center to each focus is 11, so $c = 11$. The equation for an ellipse is $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, where $a^2 = b^2 + c^2$. Given the point $(1, \frac{61\sqrt{3599}}{60})$ lies on the ellipse, solving for $a^2$ and $b^2$ gives the equation $\frac{x^2}{3600} + \frac{y^2}{3721} = 1$.

Write an Equation for the Ellipse (0,11),(0,−11)( 0,11 ) , ( 0 , - 11 )(0,11),(0,−11)

Write an Equation for the Ellipse $( 0,11 ) , ( 0 , - 11 )$