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The ellipse (x ^ 2) / 25 + (y ^ 2) / 9 = 1 passing through point a (8,1) intersects with two points P and Q to find the trajectory equation of the midpoint m of the chord PQ
Let m coordinate (x, y), P coordinate (s, t)
Then the coordinates of O (2x-s, 2y-t)
A. P, m three points collinear
(8-X)/(1-Y)=(8-S)/(1-T).(1)
P. O is on the ellipse
(S^2)/25+(T^2)/9=1 ...(2)
((2X-S)^2)/25+((2Y-T)^2)/9=1 ...(3)
(1) (2) (3) LIANLI
Eliminate s, t
The equation containing only x and Y is the trajectory equation of M
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