Question

if the distance of P x, y from the point A 3,6 and B -3,4 are equal prove that 2x+y=5

Answer 1

PA =
$\sqrt{(x - 3) ^{2} + (y - 6) ^{2} }$
PB =
$\sqrt{(x + 3) ^{2} + (y - 4) ^{2} }$
As it is given PA= PB
so PA² = PB²
(x-3)² + (y-6)² = (x+3)² + (y-4)²
x²-6x+9 + y²-12y+36 = x²+6x+9 + y²-8y+16
12x + 4y = 20
3x + y = 5