Question

If the points P(x, y) is equidistant from the points A(5, 1)and B(–1, 5), prove that 3x = 2y.

Answer 1

As per the question, we have

AP = BP

`⇒ sqrt((x -5)^2 +(y-1)^2) = sqrt((x+1)^2 +(y-5)^2)`

`⇒(x-5)^2 +(y-1)^2 = (x+1)^2 +(y-5)^2`          (Squaring both sides) 

`⇒x^2 - 10x +25 + y^2 -2y +1 = x^2 +2x +1+y^2 -10y+25`

⇒ –10x – 2y = 2x – 10y

⇒ 8y = 12x

⇒ 3x = 2y