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Question 448310: endpoints of major axis at (2,12) and (2,-4, endpoints of minor axis at (4,4)(0,4)
How do you write the equation?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! endpoints of major axis at (2,12) and (2,-4, endpoints of minor axis at (4,4)(0,4)
How do you write the equation?
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Standard form of ellipse with vertical major axis: (x-h)^2/b^2+(y-k)^2/a^2=1 (a>b)
Standard form of ellipse with horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b)
Note that a^2 and b^2 have changed places in the two forms.
This is an ellipse with a vertical major axis (First standard form listed above)
x-coordinate of center=2
y-coordinate of center=4
center (2,4)
Length of major axis=12+4=16=2a
a=8
a^2=64
length of minor axis=4=2b
b=2
b^2=4
c^2=a^2-b^2=64-4=60
c=√60=7.75
We now have enough information to write the equation of this elllipse
(x-2)^2/4+(y-4)^2/64=1
see the graph below as a visual check on the parameters above
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y=((1-(x-2)^2/4)*64)^.5+4
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