Question

If the distance of P(x, y) from A(6,2) and B(-2, 6)
are equal prove that y = 2x.​

Answer 1

$\:\: \underline{\underline{\bf{\large\mathfrak{~~Solution~~}}}}$

now as the points A and B both are at same distance from the point P so

AP=BP

now.......

$\sqrt{(x - 6) {}^{2} + (y - 2) {}^{2} } = \sqrt{(x + 2) {}^{2} + (y - 6) {}^{2} } \\ = > x {}^{2} - 12x + 36 + y {}^{2} - 4y + 4 = x {}^{2} + 4x + 4 + y {}^{2} - 12y + 36 \\ = > - 12x - 4y = 4x - 12y \\ = > 8y = 16x \\ = > y = 2x$

(proved)

$:\: \underline{\underline{\bf{\large\mathfrak{~hope ~this ~help~you~~}}}}$