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.​

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.

answer:

step-by-step explanation:

the revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. there are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). so, revenue y is given by y = (320 - 10x)(45 + 5x).