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CGP EDU Academic Team
Published on: August 13, 2026
If A (2, 0), B (–1, 0) and C (1, 3) are three points then find locus of point P satisfying the relation PA 2 + PB 2 = PC 2 .
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Sol. Let the point P (h, k)
Given PA 2 + PB 2 = PC 2
⇒ (h – 2) 2 + k 2 + (h + 1) 2 + k 2 = (h – 1) 2 + (k – 3) 2
⇒ h 2 – 4h + 4 + k 2 + h 2 + 2h + 1 + k 2
= h 2 – 2h + 1 + k 2 – 6k + 9
⇒ h 2 + k 2 + 6k – 5 = 0
∴ Locus x 2 + y 2 + 6y – 5 = 0
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