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If A, B and P are the points (-4, 3), (0, -2) and (α,β) respectively and P is equidistant from A and B, show that 8α - 10β + 21= 0.
Ans : AP = PB ⇒ AP2 = PB2
(∝ + 4)2 + (β - 3)2 = ∝2 +(β + 2)2
∝2 + 8∝ + 16 + β2 - 6β + 9 = ∝2 + β2 + 4β + 4
8∝ - 6β - 4β + 25 - 4 = 0
8∝ - 10β + 21 = 0
1 1/3:2/3:1/6
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