Question

The co-ordinate of the point on the circle $x^2+y^2–12x–4y+30=0$, which is farthest from the origin are:

• A. (9, 3)
• B. (8, 5)
• C. (12, 4)
• D. none

Answer 1

The correct option is A (9, 3)

C = (6, 2) P = (0, 0) $CP=\sqrt{40}=2\sqrt{10}$ $r=\sqrt{10}$
Farthest point B divides $\overline{CP}$ is in the ratio r : CP + r enternally
r : CP + r = 1 : 3
$B=\frac{3(6,2)-1(0,0)}{2}=(9,3)$