Question 525796: what is the equation for the ellipse with the center at (2,-2); Vertex (7,-2); and focus at (4,-2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the equation for the ellipse with the center at (2,-2); Vertex (7,-2); and focus at (4,-2)
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Given ellipse has a horizontal major axis with equation of the standard form:
(x-h)^2/a^2+(y-k)^2/b^2,a>b, with (h,k) being the (x,y) coordinates of the center.
For given ellipse:
Center: (2,-2)
From coordinates of given vertex,
Length of major axis=10=2a
a=5
a^2=25
..
From coordinates of the given focus,
c=2
c^2=4
..
c^2=a^2-b^2
b^2=a^2-c^2=25-4=21
b=√21
Equation of ellipse:
(x-2)^2/25+(y+2)^2/21=1
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