Question 573940: Find the equation of the ellipse with the following properties.
The ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8) and (0, -8).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the equation of the ellipse with the following properties.
The ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8) and (0, -8).
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Standard form of equation for an ellipse with vertical major axis:
(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For given ellipse:
Center: (0,0)
Length of vertical major axis=16=2a
a=8
a^2=64
c=6 (dstance from origin to foci on the major axis)
c^2=36
c^2=a^2-b^2
b^2=a^2-c^2=64-36=28
Equation for given ellipse:
x^2/28+y^2/64=1
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