SOLUTION: Find the equation of the ellipse if the endpoints of minor axis are (1,3) and (1,-1) with a focus at (-1,1).Express your answer in general form.

Question 1168920: Find the equation of the ellipse if the endpoints of minor axis are (1,3) and (1,-1) with a focus at (-1,1).Express your answer in general form.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

The equation of an ellipse can be given as,

where
'' represents the semi-major axis (half of the length of the major axis)
'' represents the semi-minor axis (half of the length of the minor axis)
‘’ represents the coordinate of the center
‘’ represents the coordinate of the center

if the endpoints of minor axis are (,) and (,) , minor axis length is equal to the distance between them which is
half of the length of the minor axis is
=> the center mast be half way between endpoints, and it is at (,)

a focus at (,)

the distance between foci (,) and center (,)
focus is units from the center, so

using the Pythagorean fact of all ellipses

so, your formula is

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