Question

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

Answer 1

Given, PA = PB

$\Rightarrow \sqrt{{(x-5)}^2+{(y-1)}^2}=\sqrt{{(x+1)}^2+{(y-5)}^2}$



On squaring both sides, We get-

${(x-5)}^2+{(y-1)}^2={(x+1)}^2+{(y-5)}^2$

$\Rightarrow x^2+25-10x+y^2+1-2y=x^2+1+2x+y^2+25-10y$

$\Rightarrow -10x-2y=2x-10y$

$\Rightarrow -10x-2x=-10y+2y$

$\Rightarrow 12x=8y$

$\Rightarrow 3x=2y$
Hence Proved.