Question 589347: write an equation for the ellipse with end points of the major axis at (10,2) and (-8,2), foci at (6,2) and (-4,2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! write an equation for the ellipse with end points of the major axis at (10,2) and (-8,2), foci at (6,2) and (-4,2)
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Standard form of equation for an ellipse with horizontal major axis:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k)=(x,y) coordinates of center.
For given ellipse:
y-coordinate of center=2
x-coordinate of center=1 (10-8)/2=2/2=1 (mid point formula)
center: (1,2)
length of horizontal major axis=18 (-8 to 10)=2a
a=9
a^2=81
2c=10 (-4 to 6) (Foci)
c=5
c^2=25
c^2=a^2-b^2
b^2=a^2-c^2=81-25=56
Equation of given ellipse:
(x-1)^2/81+(y-2)^2/25=1
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