- [Maximum mark: 9]
The diagram shows the curve with equation yₖ = kx² − x, k > 0, which intersects the x‑axis at the origin and at the point Aₖ(1/k, 0).
The normal to the curve at Aₖ intersects the curve again at point Bₖ.
(a) Show that the x‑coordinate of Bₖ is −1/k. [6]
Consider the case where k = 2.
(b) Calculate the finite area of the region between the curve with equation y₂ = 2x² − x and the normal at A₂. [3]