This thesis discusses the pencil of ellipse. It can be used to solve some problems of ellipse. If there are Q1 and Q2, then Q1 + kQ2 = 0 with k as parameter of real numbers to form pencil of ellipse. An equation of ellipse contain the parameter that not only produce an ellipse, but it forms lines, circle, parabola and hyperbola as well. There are some special conditions from pencils of elliā¦