If the chord of contact of tangents from a point P to the  parabola y2=4ax touches the parabola x2=4by, then the  locus of P is

The chord of contact of the parabola y2=4ax w.r.t. point Px1,y1 is yy1=2ax+x1-------(1) This line touches the parabola x2=4by .  Solving (1) with parabola, we have x2=4b2ay1x+x1 or  y1x2−8abx−8abx1=0According to the question, this equation must have equal roots.Therefore, D = 0 or     64a2b2+32abx1y1=0 or     x1y1=−2ab or xy=−2abwhich is the required locus.