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Question 557598: Find an equation for an ellipse with major axis of length 10 and foci at (0,-4) and (-4,-4).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find an equation for an ellipse with major axis of length 10 and foci at (0,-4) and (-4,-4)
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Standard form of equation for ellipse with horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2, a>b, (h,k) being the (x,y) coordinates of the center.
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For given equation:
major axis: horizontal (from foci data)
y-coordinate of center:-4 (from foci data)
x-coordinate of center:-2 (midway between foci)
center: (-2,-4)
length of horizontal major axis=10=2a
a=5
a^2=25
c=2 (distance from center to focus)
c^2=4
c^2=a^2-b^2
b^2=a^2-c^2=25-4=21
b=√21≈4.58
Equation of given ellipse:
(x+2)^2/25+(y+4)^2/21
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