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A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA2 – PB2 = 13. - Mathematics and Statistics

Sum

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA2 – PB2 = 13.

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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.

Concept: Equation of Locus
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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 5 Locus and Straight Line
Exercise 5.1 | Q 5 | Page 67
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