# analytic geometry: equation of the locus

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analytic geometry: equation of the locus

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.?

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

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

Continue simplifying this equation. Good luck.