3.2: Tangent to a circle and a related circle through the origin

0606/12/M/J/25 — Question 3 · 8 marks

A circle with centre CC has the equation x2+y2−10x−4y+24=0x^{2} + y^{2} - 10x - 4y + 24 = 0.
(a)
Show that the line y=2x−3y = 2x - 3 is a tangent to this circle.
[3]
(b)
Given that this tangent touches the circle at the point PP, find the coordinates of PP.
[2]
(c)
Find the equation of the circle which has its centre at PP and passes through the origin.
[3]