# analytic geometry: equation of the locus

hey i need your help. please answer this question.please

1.a point moves so that the product of the distance from (0,6) and (9,0) is twice the ratio of its ordinate to its abscissa .find the equation of the locus.?

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## $\sqrt{x^2 + (y - 6)^2}

$\sqrt{x^2 + (y - 6)^2} \times \sqrt{(x - 9)^2 + y^2} = 2\times\dfrac{y}{x}$

$\left[ x^2 + (y - 6)^2 \right] \times \left[ (x - 9)^2 + y^2 \right] = \dfrac{4y^2}{x^2}$

Continue simplifying this equation. Good luck.