Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11).
A) $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 120 } = 1$
B) $\frac { x ^ { 2 } } { 120 } - \frac { y ^ { 2 } } { 121 } = 1$
C) $\frac { x ^ { 2 } } { 120 } + \frac { y ^ { 2 } } { 121 } = - 1$
D) $\frac { x ^ { 2 } } { 120 } + \frac { y ^ { 2 } } { 121 } = 1$
E)none of these

Question

Write the equation of the ellipse that has its center at the origin with focus at (0, 1) and vertex at (0, 11). 
A) $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 120 } = 1$
B) $\frac { x ^ { 2 } } { 120 } - \frac { y ^ { 2 } } { 121 } = 1$
C) $\frac { x ^ { 2 } } { 120 } + \frac { y ^ { 2 } } { 121 } = - 1$
D) $\frac { x ^ { 2 } } { 120 } + \frac { y ^ { 2 } } { 121 } = 1$
E)none of these

Quizplus · Accepted Answer

The ellipse is vertical with center at the origin, vertex at (0, 11), and focus at (0, 1). The distance from the center to the vertex is 11, so $b^2 = 121$. The distance from the center to the focus is 1, so $c^2 = 1$. Using the relationship $a^2 = b^2 - c^2$, we find $a^2 = 120$. The equation is $\frac{x^2}{120} + \frac{y^2}{121} = 1$.

Write the Equation of the Ellipse That Has Its Center x2121+y2120=1\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 120 } = 1121x2​+120y2​=1

Write the Equation of the Ellipse That Has Its Center $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 120 } = 1$