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If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB. - Mathematics and Statistics

Sum

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

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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.

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 1 | Page 67
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