Let S be the focus of the conic, PX the directrix, e the eccentricity.
Let V be the middle point of PP′.
Draw VK perpendicular to the directrix, and with centre V describe a circle, radius equal to e.VK.
Join SP, SP′ and draw radii Vp, Vp′, parallel to SP′, SP, and let PP′ meet the directrix in L. Then p, p′ are on the line SL.