A point moves so that the sum of the squares of its distances from two intersecting straight lines is constant. Prove that its locus is an ellipse.

Explanation

OA and DB

`y=ntantheta,y=-xtantheta`

`xsintheta-ycostheta=0`

`xsintheta+ycostheta=0`

`PL^2+PM^2=lambda^2`(const)

`((hsintheta-kcostheta)/sqrt(sin^2theta+cos^2theta))^2+((hsintheta+kcostheta)/sqrt(sin^2theta+cos^2theta))^2=lambda^2`

`h^2sin^2theta+k^2cos^2theta=lambda^2`

`h^2/((lambda^2)/(sin^2theta))+k^2/((lambda^2/cos^2theta))=1`

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