Question 589451: Write an equation for an ellipse that satisfies each set of conditions.
endpoints of major axis at (3, -8) and (3, 4), foci at (3, -2+2  ) and (3, -2- )
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation for an ellipse that satisfies each set of conditions.
endpoints of major axis at (3, -8) and (3, 4), foci at (3, -2+2√5) and (3, -2-√5)
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I will assume the 2nd given end point for the foci is (3,-2-2√5), not (3, -2-√5), as stated.
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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)=(x,y) coordinates of center.
For given ellipse:
x-coordinate of center=3
y-coordinate of center=-2 (by midpoint formula)
center: (3,-2)
length of vertical major axis=12=2a (from -8 to 4)
a=6
a^2=36
c=2√5 ( from foci)
c^2=20
c^2=a^2-b^2
b^2=a^2-c^2=36-20=16
b=4
Equation of given ellipse:
(x-3)^2/16+(y+2)^2/36=1
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