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

Answer:

AP=BP

TAKING SQUARING ON BOTH SIDES

${ap}^{2} = {bp}^{2}$

USING DISTANCE FORMULA

${(x1 - x2)}^{2} + (y1 - y2) = {(x1 - x2)}^{2} + {(y1 - y2)}^{2} \\ {(5 - x)}^{2} + {(1 - y)}^{2} = {( - 1 - x)}^{2} + {(5 - y)}^{2} \\ 25 + {x}^{2} - 10x + 1 + {y}^{2} - 2y = 1 + {x}^{2} + 2x + 25 + {y}^{2} - 10y \\ - 10x - 2y = 2x - 10y \\ - 10x - 2x = - 10y + 2y \\ - 12x = - 8y \\ 12x = 8y \\ 4(3x) = 4(2y) \\ 3x = 2y$

HENCE PROVED

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