Question

Q.10. if the distances of p(x, y) from a(5, 1) and b(– 1, 5) are equal, then prove that 3x =2y.

Answer 1

From the Question,

AP = BP  ⇒ AP² = BP²  where P(x,y) A(5,1) B(-1,5)

Distance = √(x₂-x₁)²+(y₂-y₁)²

As the distances are squared then the roots get cancelled.

(5-x)² + (1-y)² = (-1-x)² + (5-y)²

25+x²-10x+1+y²-2y = 1+x²+2x+25+y²-10y

The equivalent values on both sides get cancelled.

                12x = 8y

(÷) 4 ⇒      3x = 2y
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