The correct option is A xy=−2ab
Let P≡(h,k)
Equation of chord of contact for parabola y2=4ax is
yk=2a(x+h)
⇒y=2axk+2ahk ⋯(1)
Equation of tangent for x2=4by will be of form y=mx−bm2 ⋯(2)
As equation (1) and (2) represent the same line, so,
m=2ak and
2ahk=−bm2
⇒2ahk=−b(2ak)2
⇒hk=−2ab
Hence, the locus of the point P will be xy=−2ab