Question 454540: Write an equation for each ellipse described below:
the endpoints of the major axis are at (10,2) and (-8,2). The foci are at (6,2) and (-4,2).
I have found that the center is at (1,2), but this may be wrong.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation for the ellipse described below:
the endpoints of the major axis are at (10,2) and (-8,2). The foci are at (6,2) and (-4,2).
I have found that the center is at (1,2), but this may be wrong.
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Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1, (a>b), with (h,k) being the (x,y) coordinates of the center.
The difference between the two forms is the interchange of a^2 and b^2.
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Major axis and foci located on the line, y=2, shows that this ellipse has a horizontal major axis, with center at (1,2) as you correctly figured out.
Center (1,2)
length of major axis=18=2a
a=9
a^2=81
2c=10
c=5
c^2=25
c^2=a^2-b^2
b^2=a^2-c^2=81-25=56
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Equation:
(x-1)^2/81+(y-2)^2/56=1
See the graph below for a visual check on the answers.
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y=(56-56(x-1)^2/81)^.5+2
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