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Question 556579: Can you please help with this problem?:
"Find the constant sum of an ellipse with the given foci and point of the ellipse. co-vertex(o,-8), focus(6,0)"
That is my entire question. I don't need you to tell me the answer but if you could explain how to do it, that would be excruciatingly helpful. :)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! "Find the constant sum of an ellipse with the given foci and point of the ellipse. co-vertex(o,-8), focus(6,0)"
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Given data shows this is an ellipse with horizontal major axis. Standard form of its equation:
(x-h)^2/a^2+(y-k)^2/b^2, a>b, (h,k) being the (x,y) coordinates of the center.
For given equation:
x-coordinate of center=0 (from focus)
y-coordinate of center=0 (from co-vertex)
center: (0,0)
length of co-vertex=16=2b
b=8
b^2=64
c=6 (center to focus)
c^2=36
c^2=a^2-b^2
a^2=c^2+b^2=36+64=100
a=√100=10
Equation of given ellipse:
x^2/100+y^2/64=1
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