If the distance of P(x,y) from A(5,1) and B(-1,5) are equal, then prove that 3x = 2y.

A(5,1)≡(x1,y1) B(-1,5)≡(x2,y2) P≡(x,y)
PA=PB(given)
∴By distance formula √(x-x1)²+(y-y1)² we have,
⇒(x-5)²+(y-1)²=(x+1)²+(y-5)²
⇒x²-10x+25+y²-2y+1=x²+2x+1+y²-10y+25
∴-10x-2y=2x-10y
∴-12x=-8y
2y=3x. [hence proved]