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Question
If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.
Solution
Let P(x, y) be any point on the required locus.
Given, A(2, 0), B(0, 3) and
AP = 2BP
∴ AP2 = 4BP2
∴ (x – 2)2 + (y – 0)2 = 4[(x – 0)2 + (y – 3)2]
∴ x2 – 4x + 4 + y2 = 4(x2 + y2 – 6y + 9)
∴ x2 – 4x + 4 + y2 = 4x2 + 4y2 – 24y + 36
∴ 3x2 + 3y2 + 4x – 24y + 32 = 0
∴ The required equation of locus is
3x2 + 3y2 + 4x – 24y + 32 = 0
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