The co-ordinate of a point on the parabola y2=8x  whose distance from the circle x2+(y+6)2=1  is minimum is

Any point on the parabola y2=8x(4a=8 or a=2)  is (at2,2at) or (2t2,4t). For its  minimum distance from the circle means its distance from the center  (0,−6)  of the circle.Let D be the distance , thenz=D2=(2t2)2+(4t+6)2=4(t4+4t2+12t+9) ∴dzdt=4(4t3+8t+12)=0 ⇒16(t3+2t+3)=0 ⇒16(t+1)(t2−t+3)=0 ⇒t=−1 d2zdt2=16(3t2+2)= Positive hence minimum.∴point is (2,−4).