analytical geometry

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the axes are rectangular and a point P moves on the fixed plane lx+my+nz=p.the plane through P perpendicular to OP meets the axes in A,B,C parallel to YOZ,ZOX,XOY intersect in Q.show that the locus of Q is
p{1/x2+1/y2+1/z2}=l/x+m/y+n/z

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