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 standard equation for an ellipse with center at the origin is 
x^2/a^2 + y^2/b^2 = 1, where a is the distance from the center to a vertex and b is the distance from the center to the co-vertex.

Since the vertex is at (0,11), we know that a = 11.

The distance from the center to a focus is c, where c^2 = a^2 - b^2.

We are given that one focus is at (0,1), so we know c = 1.

Plugging in these values, we get: 
1^2(x^2/11^2) + 1^2(y^2/b^2) = 1 
x^2/121 + y^2/b^2 = 1

Multiplying both sides by 121, we get: 
x^2 + 121y^2/b^2 = 121

So the equation in the standard form is  x^2 + 121y^2/121 = 1, which simplifies to x^2 + y^2/1 = 1.

Therefore, the correct choice is D: 11ea99db_b857_a38a_94ac_f59a1307e0bb_TB4590_11.

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 $\frac { x ^ { 2 } } { 121 } + \frac { y ^ { 2 } } { 120 } = 1$