(b) Figure 3 shows a sketch of the curve C with equation = 3 -

2

. It passes

through the origin O and the point B on the x-axis.

(i) Find, in the form + + = 0, an equation of the normal to C at

the point A (1, 2).

[3 marks]

(ii) Show that this normal passes through the point B.

[2 marks]

The shaded region R is bounded by the curve and the line AB.

(iii) Find, by integration, the area of R.

[5 marks]

(b) Figure 3 shows a sketch of the curve C with equation y = 3x - x2. It passes through the origin O and the point B on the x-axis. (1) Find, in the form ax + by + c = 0, an equation of the normal to Cat the point A (1, 2). [3 marks] (ii) Show that this normal passes through the point B. [2 marks] The shaded region R is bounded by the curve and the line AB. (iii) Find, by integration, the area of R. [5 marks] WUC114/05 A(1, 2) Figure 3