Locus
2011-03-13 6:20 am
Given points F(3,0) and G (-3,0) with PF + PG = 10, find the equation of the locus of point P.
回答 (1)
2011-03-13 6:36 am
✔ 最佳答案
Let P = (x,y)PF + PG = 10=> √[(x – 3)^2 + y^2 ] + √[(x + 3)^2 + y^2] = 10=>√[(x – 3)^2 + y^2]) = 10 – √[(x + 3)^2 + y^2]=> x^2 – 6x + 9 + y^2 = 100 –20√[(x + 3)^2 + y^2] + x^2 + 6x + 9 + y^2=> 20√[(x + 3)^2 + y^2] = 100 + 12x=> 5√[(x + 3)^2 + y^2] = 25 + 3x=> 25x^2 + 150x + 225 + 25y^2 = 625 + 150x + 9x^2=> 16x^2 + 25y^2 = 400=> x^2/25 + y^2/16 = 1
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