if a b and p are the points -4 3 0 -2 and, Mathematics

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if a b and p are the points -4 3 0 -2 and

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

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