Question 7 A circle, C1, passes through the points A(4, 0) and B(0,8). Its centre, P, lies on the line
y = x + 1.
(a) (i) Show that the centre of the circle, Ci is (4, 5).
(ii) Hence find the equation of the circle, C.
(b) A second circle, C2, with the equation x2 + y2 + ax + by + 32 = 0, has the same
centre, P, as circle C.
(i) Find the value of a and of b.
(ii) Show that the circle C2 lies within the circle Ci.​