SOLUTION: Write an equation for the ellipse, satisfying the following conditions. Foci at (0,-2) and (0,2); the point (-3,2) on ellipse

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Question 970479: Write an equation for the ellipse, satisfying the following conditions.
Foci at (0,-2) and (0,2); the point (-3,2) on ellipse
Found 2 solutions by josgarithmetic, lwsshak3:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
There is a value c, the distance from the center to either focus. Your ellipse has center at the origin, (0,0). The value for c is .

Standard Form for the ellipse is , and there is a relationship among a, b, and c:

You have a given point on the ellipse, (-3,2). This means you have an equation,

You also know c=2, so you have another equation, ,
.

The two equations outlined in green border give you a system of equations to solve for and , and you can then finish writing your ellipse equation with its values.

Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
Write an equation for the ellipse, satisfying the following conditions.
Foci at (0,-2) and (0,2); the point (-3,2) on ellipse
***
Given ellipse has a vertical major axis with center at the origin
Its standard form of equation: . a>b
center: (0, 0)
c=2 (distance from center to foci)
c^2=a^2-b^2
4=a^2-b^2
b^2=a^2-4
solving for a^2 and b^2 using coordinates from given point(-3, 2) on the ellipse
plug in coordinates:

lcd: a^2(a^2-4)
9a^2+4(a^2-4)=a^4-4a^2
9a^2+4a^2-16=a^4-4a^2
a^4-17a^2+16=0
(a^2-16)(a^2-1)=0
..
a^2-16=0
a^2=16
b^2=a^2-4=16-4=12
or
a^2-1=0
a^2=1
b^2=a^2-4=1-4=-3
b^2≠-3(reject, a^2=1)
..
equation: