The correct option is D 4
Given parabola is y2=x
Any point on the parabola is (t24,t2)
Comparing with the coordinates of P(t),
(t24,t2)=(4,−2)⇒t=−4
As PQ is focal chord, so coordinates of Q(−1t) is (14t2,−12t)=(164,18)
Now, equation of tangent at Q is T=0
⇒y×18=12(x+164)⇒y=4x+116
Hence, the slope of the tangent at Q is 4.