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Question
If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.
Solution
Let P(x, y) be any point on the required locus.
Given, A(1, 3) and B(2, 1).
PA = PB
∴ PA2 = PB2
∴ (x – 1)2 + (y – 3)2 = (x – 2)2 + (y – 1)2
∴ x2 – 2x + 1 + y2 – 6y + 9 = x2 – 4x + 4 + y2 – 2y + 1
∴ –2x – 6y + 10 = –4x – 2y + 5
∴ 2x – 4y + 5 = 0
∴ The required equation of locus is 2x – 4y + 5 = 0.
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