finding equation of ellipse

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March 8, 2013 - 6:28am
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andilim984
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finding equation of ellipse

an ellipse with directrix y+22/3=0,center at (4,1) and one focus at (4,-2).

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March 8, 2013 - 6:47am
Aedan Lee's picture
Aedan Lee
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Joined: Feb 21 2013 - 11:07am
Points: 126
Re: finding equation of ellipse

(x - h)^2 / b^2 + (y - k)^2 / a^2 = 1

(h, k) = (4, 1)
d = 22/3
c = distance between (4, 1) and (4, -2) = 3

e = c/a
d = a/e = a/(c/a) = a^2 / c
22/3 = a^2 / 3
a^2 = 22

b^2 + c^2 = a^2
b^2 + 3^2 = 22
b^2 = 13

(x - 4)^2 / 13 + (y - 1)^2 / 22 = 1

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