If A(2, 0), B(–2, 0) and C(3, –3) are three points then fin…

Maths Rectangular Cartesian Co-ordinates Transformation of Axes and Locus Subjective Type

Published on: August 13, 2026

If A(2, 0), B(–2, 0) and C(3, –3) are three points then find the locus of a point P which satisfies the relation :

PA 2 + PB 2 = 2PC 2

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Sol. Let P(h, k) and A(2, 0), B(–2, 0), C(3, –3)

Given PA 2 + PB 2 = 2PC 2 ⇒ (h – 2)

2 + (k – 0) 2 + (h + 2) 2 + (k – 0) 2 = 2[(h – 3)

2 + (k + 3) 2 ]

⇒ 2h 2 + 2k 2 = 2h 2 + 2k 2 – 12h + 12k + 36

⇒ 12h – 12k – 36 = 0

⇒ h – k – 3 = 0

locus x – y – 3 = 0

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