# Tangents and Areas

**Calculus**Level pending

A tangent is drawn at a point \(P1\) on the curve \(y=x^3\).The tangent intersects the curve again at point \(P2\). Another tangent is drawn at the point \(P2\),it intersects the curve at \(P3\) and so on.Prove that the \( abcissae\) of the pts. \(P1, P2,...\)are in \(GP\) and find the ratio: \(\dfrac{Area(\Delta (P1P2P3))}{Area(\Delta(P2P3P4)}\)