Coordinate Geometry-13

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A point moves so that its distance from the point (2, 0) is three times its distance from (-3, 0). Find the locus of the point.

Solution: Let A be the point (2, 4)

Let B be the point (- 3, 0)

Let P be the point (x, y)

PA = 3 PB

=> √(x - 2)2 + (y - 4)2 = √3 [ (x + 3)2 + (y - 0)2 ]

i.e. (x - 2)2 + (y - 4)2 = 9 [ (x + 3)2 + (y - 0)2 ] [squaring both sides]

i.e. x2 + y2 - 4x - 8y + 20 = 9 [x2 + y2 + 6x + 9 ]

i.e. 8x2 + 8y2 + 58x + 8y + 61 = 0 is the equation of the locus.

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