Question

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

Answer 1

Answer:

$3x = 2y.$

Step-by-step explanation:

$\sqrt{ {(x - 5)}^{2} + {(y - 1)}^{2} } = \sqrt{ {(x + 1)}^{2} + {(y - 5)}^{2} } \\ \\ {(x - 5)}^{2} + {(y - 1)}^{2} = {(x + 1)}^{2} + {(y - 5)}^{2} \\ \\ {x}^{2} + 25 - 10x + {y}^{2} + 1 - 2y = {x}^{2} + 1 + 2x + {y}^{2} + 25 - 10y \\ \\ 26 - 10x - 2y= 26 + 2x - 10y \\ \\ - 12x = - 8y \\ \\ 3x = 2y.$