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It is given that P is equidistant from A and B.
So, PA = PB
PA2 = PB2
Using distance formula, we have:
(x - 5)2 + (y - 1)2 = (x + 1)2 + (y - 5)2
x2 + 25 - 10x + y2 + 1 - 2y = x2 + 1 + 2x + y2 + 25 - 10y
- 12x = -8y
3x = 2y
Hence proved.
So, PA = PB
PA2 = PB2
Using distance formula, we have:
(x - 5)2 + (y - 1)2 = (x + 1)2 + (y - 5)2
x2 + 25 - 10x + y2 + 1 - 2y = x2 + 1 + 2x + y2 + 25 - 10y
- 12x = -8y
3x = 2y
Hence proved.
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