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Question
A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA2 – PB2 = 13.
Solution
Let P(x, y) be any point on the required locus.
Given, A(2, 4), B(5, 8) and
PA2 – PB2 = 13
∴ [(x – 2)2 + (y – 4)2] – [(x – 5)2 + (y – 8)2] = 13
∴ (x2 – 4x + 4 + y2 – 8y + 16) – (x2 – 10x + 25 + y2 – 16y + 64) = 13
∴ 6x + 8y – 69 = 13
∴ 6x + 8y – 82 = 0
∴ 3x + 4y – 41 = 0
∴ The required equation of locus is
3x + 4y – 41 = 0.
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