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Question 406971: My problem says: find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse.
(x-8) squared over 144 + (y-2) squared over 81 =1
I understand the center is (8,2) but I do not understand how to find the foci and the endpoints of the major and minor axes. Thank you so much, I appreciate it.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! My problem says: find the coordinates of the center and foci and the lengths of the major and minor axes for the ellipse with the given equation. Then graph the ellipse.(x-8) squared over 144 + (y-2) squared over 81 =1 I understand the center is (8,2) but I do not understand how to find the foci and the endpoints of the major and minor axes. Thank you so much, I appreciate it.
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Standard forms of an ellipse:
(x-h)^2/a^2+(y-k)^2/b^2=1 (major axis horizontal)
(y-k)^2/a^2+(x-h)^2/b^2=1 (major axis vertical)
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Given equation is of the first form:
(x-8)^2/144+(y-2)^2/81=1
This is an ellipse with a horizontal major axis with center(8,2)
a^2=144
a=12
b^2=81
b=9
c=sqrt(a^2-b^2)=sqrt(144-81)=sqrt(83)=9.11
Length of major axis=2a=24
Length of minor axis=2b=18
Measuring from the center(8,2), the endpoints
vertices =(8+-a,2)=(8+-12,2)=(20,2),(-4,2)
foci=(8+-c,2)=(8+-9.11,2)=(17.11,2),(-1.11,2)
minor axis=(8,2+-b)=(8,2+-9)=(8,11),(8,-7)
With data from above, your graph should look like the graph below:
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2+(81-(81(x-8)^2)/144)^.5
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