6. The circle C has equation
x2 + y2 - 6x + 4y = 12
(a) Find the centre and the radius of C.
The point P(–1, 1) and the point Q(7, –5) both lie on C.
(b) Show that PQ is a diameter of C.
The point R lies on the positive y-axis and the angle PRQ = 90°.
(c) Find the coordinates of R.
7. (i) Solve, for –180° ≤ θ < 180°,
(1 + tanθ)(5 sinθ - 2) = 0
(ii) Solve, for 0 ≤ x < 360°,
4sin x = 3tan x.
8. (a) Find the value of y such that
log2 y = –3
(b) Find the values of x such that
(log2 32 + log2 16)/log2 x = log2 x
Figure 2 shows a closed box used by a shop for packing pieces of cake. The box is a right
prism of height h cm. The cross section is a sector of a circle. The sector has radius r cm
and angle 1 radian.
The volume of the box is 300 cm3
(a) Show that the surface area of the box, S cm2 , is given by S = r2 + 1800/r
(b) Use calculus to find the value of r for which S is stationary.
(c) Prove that this value of r gives a minimum value of S.
(d) Find, to the nearest cm2, this minimum value of S.