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Question
Find the relation between a and b if the point P(a ,b) is equidistant from A (6,-1) and B (5 , 8).
Solution
Given , PA = PB
∴ PA2 = PB2
⇒ (a - 6)2 + (b + 1)2 = (a - 5)2 + (b - 8)2
⇒ a2 + 36 - 12a + b2 + 1 + 2b = a2 + 25 - 10 a + b2 + 64 - 16 b
⇒ -2a + 18b - 52 = 0
⇒ -a + 9b - 26 = 0
⇒ a = 9b - 26
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