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Question
If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA2 = 3PB2.
Solution
Let P(x, y) be any point on the required locus.
Given, A(4, 1), B(5, 4) and
PA2 = 3PB2
∴ (x – 4)2 + (y – 1)2 = 3[(x – 5)2 + (y – 4)2]
∴ x2 – 8x + 16 + y2 – 2y + 1 = 3(x2 – 10x + 25 + y2 – 8y + 16)
∴ x2 – 8x + y2 – 2y + 17 = 3x2 – 30x + 75 + 3y2 – 24y + 48
∴ 2x2 + 2y2 – 22x – 22y + 106 = 0
∴ x2 + y2 – 11x – 11y + 53 = 0
∴ The required equation of locus is
x2 + y2 – 11x – 11y + 53 = 0.
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