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Question 979651: 1. Find an equation of the ellipse that has center
(−2,5) a minor axis of length 2 and a vertex at
(−4,5)
2. Find an equation of the ellipse having a major axis of length 6 and foci at
(6,3)and (2,3)
.
Answer by zuproc66(2)   (Show Source):
You can put this solution on YOUR website! Ellipse is the locus point which moves so that the sum of its distances from two fixed points is constant and is equal to the length of the major axis (2a)
1. General Eqn: Ax^2 + Cy^2 + Dx + Ey + F = 0
2. Standard Eqn
Center at origin C(0,0)
[(x^2/a^2) + (y^2/b^2)] =1 major axis - horizontal
[(x^2/b^2) + (y^2/a^2)] =1 major axis - vertical
Center at (h,k) C(h,k)
[(x-h)^2/a^2) + ((y-k)^2/b^2)] =1 major axis - horizontal
[(x-h)^2/b^2) + ((y-k)^2/a^2)] =1 major axis - vertical
note: a > b
now substituting values
((x + 2)^2)/4) + ((y-5)^2)/5))=1 - eqn of the ellipse
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