A point moves so that the distance between the foot of perpendiculars from it on the lines $a{x}^2+2hxy+b{y}^2=0$ is a constant $2d$ . Show that the equation to its locus is $\left(x^2+y^2\right)\left(h^2-ab\right)=d^2\left\{{\left(a-b\right)}^2+4h^2\right\}\dot{}$

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