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Question 458613: An ellipse has a vertex at (4,4) And a covertex at (2,5). Please find its equation in standard for and give the coordinates of the two focus points.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! An ellipse has a vertex at (4,4) And a covertex at (2,5). Please find its equation in standard for and give the coordinates of the two focus points.
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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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If you plot these two points you can see that this ellipse has a horizontal major axis and a center at (2,4) (First form listed above)
length of major axis=4=2a
a=2
a^2=4
length of minor axis=2b
b=1
b^2=1
c^2=a^2-b^1=4-1=3
c=√3=1.732
Foci: (2±√3,4)
Equation:
(x-2)^2/4+(y-4)^2=1
see graph below as a visual check on the answer.
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y=(1-(x-2)^2/4)^.5+4
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