This thesis discusses the pencil of parabola. Given two parabolas l1 and l2 and we have l1 + kl2 = 0 with real-valued k and k 6= −1 performing a pencil of parabola through the points of intersection of two parabolas. This thesis also discusses the existence of a parabola and a special cases such as the pencil of parabola passing through a point, pencil of parabola touching the axis of sy…