We have C1 : y2 = 4x (1) C2 : x2+y2 - 6x + 1 = 0 (2) Substituting y2 = 4x in Eq. (2), we get x2 + 4x - 6x + 1 = 0 x2 - 2x + 1 = 0 x = 1 That is, the points of intersection of the circle and the parabola are (1, 2) and (1, –2).
Clearly, C1 and C2 touch each other exactly at two points.
