MathDB

3

Part of 2008 IMS

Problems(1)

Maximum area

Source: IMS 2008

5/10/2008
Let A,B A,B be different points on a parabola. Prove that we can find P1,P2,…,Pn P_1,P_2,\dots,P_{n} between A,B A,B on the parabola such that area of the convex polygon AP1P2…PnB AP_1P_2\dots P_nB is maximum. In this case prove that the ratio of S(AP1P2…PnB) S(AP_1P_2\dots P_nB) to the sector between A A and B B doesn't depend on A A and B B, and only depends on n n.
geometryconicsparabolaratiofunctioncalculusderivative