Question 481810: Find the standard form of the equation of each ellipse satisfying the given conditions.
Endpoints of major axis: (2,2) and (8,2)
Endpoints of minor axis: (5,3) and (5,1)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the standard form of the equation of each ellipse satisfying the given conditions.
Endpoints of major axis: (2,2) and (8,2)
Endpoints of minor axis: (5,3) and (5,1)
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Given points show this is an ellipse with horizontal major axis of the standard form:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, with (h,k) being the center.
For given ellipse:
Center: (5,2) (notice that the y-coordinates(2) of the end points of the major axis do not change, and likewise, the x-coordinates(5) of the end points of the minor axis do not change.)
..
Length of major axis=8-2=6=2a
a=3
a^2=9
Length of minor axis=3-1=2
b=1
b^2=1
..
Equation: (x-5)^2/9+(y^2)^2/1=1
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