The correct option is B y2(x+2a)+4a3=0
If (h,k) be the point of intersection of tangents then the equation of chord of contact is ky=2a(x+h)⋯(1)
Equation of normal y=mx−2am−am3⋯(2)
Since both the equations are same, so by comparing we get,
m=2ak, and
2ahk=−2am−am3
⇒2ahk=−2a(2ak)−a(2ak)3
⇒k2(h+2a)=−4a3
∴ The required locus is y2(x+2a)+4a3=0