Question

If the distance of p,(x,y)from a(5,1)and b(-1,5)are equal,then prove that 3x=2y

Answer 1

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the distance of p,(x,y)from a(5,1)and b(-1,5)are equal....

therefore...pa=pb

now......

$pa = \sqrt{(5 - x) {}^{2} + (y - 1) {}^{2} } \\ pb = \sqrt{(x + 1) {}^{2} + (y - 5) {}^{2} } \\ now \: \: \: \\ pa = pb \\ \sqrt{(5 - x) {}^{2} + (y - 1) {}^{2} } = \sqrt{(x + 1) {}^{2} + (y - 5) {}^{2} } \\ = > (5 - x) {}^{2} + (y - 1) {}^{2} =( x + 1) {}^{2} + (y - 5) {}^{2} \\ = > 25 - 10x + x {}^{2} + y {}^{2} - 2y + 1 = x {}^{2} + 2x + 1 + y {}^{2} - 10y + 25 \\ = > - 10x - 2y = 2x - 10y \\ = > 8y = 12x \\ = > 3x = 2y \: \: (proved)$

$\underline{\large\mathcal\red{hope\: this \: helps \:you......}}$