The length of the perpendiculars from the focusand the extremities of a focal chord of a parabolaon the tangent at the vertex form

y2=4ax be the parabola, Pat2,2at,Qat2,−2atand the focus is S(a,0) The tangent at the vertexis x = 0. Lengths of the perpendicular from P,Q and S on this tangent are respectively l1=at2, l2=alt2,l3=a so that l1l2=a2=l32⇒l1,l2,l3 form a G.P.