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

The correct answer is: a hyperbola

Let Point P be (p, q) then equation of  equation chord of contact drawn to y² = 4ax is  y.q = 2a(x +p)
As chord of contact touches of y2 = 4ax the parabola x2 = 4by
which means chord of contact touches of y2 = 4ax the tangent to parabola x2 = 4by
As it touches x2 = 4by,  then equation of line the tangent to x2 = 4by is 
y.q = 2a(x +p) 
comparing equation and get m =  and 
then 
Therefore, the locus of point p is Hyperbola with equation xy =-2ab