The correct option is C 5y2=8(x−4)
Let (x1,y1) be point on y2=−8(x+4).
Then equation of chord of contact is T=0
i.e., 2x−y1y+2x1=0 ⋯(1)
Let P(h,k) be its mid-point.
Then its equation will be
T=S1
2x−ky+2h=k2−4h
⇒2x−ky+k2−2h=0 ⋯(2)
Comparing (1) and (2), we get
k=y1, 2x1=k2−2h
So, k2=−4(k2−2h+8)
⇒k2=85(h−4)
Hence, locus of mid-point of chord of contact is 5y2=8(x−4)