Question 456904: What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the equation of the ellipse with foci (0, 4), (0, -4) and vertices (0, 8), (0, -8)
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Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of a^2 and b^2
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Because the given x-coordinates of foci and vertices are the same at x=0, ellipse has a vertical major axis.
length of major axis=16=2a
center at (0,0) (midpoints of vertices and foci)
a=8
a^2=64
c=half the distance between foci=8/2=4
c^2=16
c^2=a^2-b^2
b^2=a^2-c^2=64-16=48
b√48=6.93..
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Equation:(x-0)^2/48+(y-0)^2/64=1
=x^2/48+y^2/64=1
see graph below as a visual check on the answers. note the center and end points of the ellipse.
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y=(64-64(x^2)/48)^.5
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