Any tangent to parabola y2 = 8x is y = mx + m2 ... (i) It touches the circle x2+y2 - 12x + 4 = 0 if the length of perpendicular from the centre (6,0) is equal to radius 32 ∴ m2+16m+m2 = ± 32 ⇒ (3m+m1)2 = 8 (m2+1) ⇒ (3m2+1)2 = 8 (m4+m2) ⇒ m4−2m2 + 1 = 0 ⇒ m = ± 1 Hence, the required tangents are y = x + 2 and y = - x - 2.