Question 857687: determine the standard equation of the ellipse that has the ends of its minor axis at (5;-3)and(5;1), and has an eccentricity of e=1/4 Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! determine the standard equation of the ellipse that has the ends of its minor axis at (5;-3)and(5;1), and has an eccentricity of e=1/4
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Given ellipse has a vertical major axis.
Its standard form of equation:
y-coordinate of center=-1(midway between -3 and 1 on the major vertical axis.)
x-coordinate of center=5
center: (5,-1)
length of minor axis=4=2b
b=2
b^2=4
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eccentricity=1/4=c/a
c=a/4
c^2=a^2-b^2
a^2/16=a^2-4
a^2-a^2/16=4
15a^2/16=4
15a^2=64
a^2=64/15
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Equation of given ellipse:
(