Find the standard form of the equation of the ellipse with the given characteristics.
Foci: $( 0,0 ) , ( 0,6 )$ ; major axis of length 12.

A) $\frac { x ^ { 2 } } { 27 } - \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 27 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$
E) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$

Question

Find the standard form of the equation of the ellipse with the given characteristics. 
Foci: $( 0,0 ) , ( 0,6 )$ ; major axis of length 12.

A) $\frac { x ^ { 2 } } { 27 } - \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$
B) $\frac { x ^ { 2 } } { 36 } + \frac { ( y - 3 ) ^ { 2 } } { 9 } = 1$
C) $\frac { x ^ { 2 } } { 27 } + \frac { ( y - 3 ) ^ { 2 } } { 36 } = 1$
D) $\frac { x ^ { 2 } } { 9 } + \frac { ( y + 3 ) ^ { 2 } } { 36 } = 1$
E) $\frac { x ^ { 2 } } { 27 } + \frac { y ^ { 2 } } { 36 } = 1$

Quizplus · Accepted Answer

The center of the ellipse is at (0,3), and the major axis is vertical with length 12, so $b^2 = 36$. The distance between the foci is 6, so $c = 3$. Using $c^2 = a^2 - b^2$, we find $a^2 = 27$. The equation is $\frac{x^2}{27} + \frac{(y-3)^2}{36} = 1$.

Find the Standard Form of the Equation of the Ellipse (0,0),(0,6)( 0,0 ) , ( 0,6 )(0,0),(0,6)

Find the Standard Form of the Equation of the Ellipse $( 0,0 ) , ( 0,6 )$