A circle C has centre D and equation

x² + y² + 2x – 8y + 8 = 0.

(a) Find the coordinates of D and the radius of C. [3]

(b) A line is drawn through the point P (4, 6) so that it touches the circle C at the point T.

(i) Show that PT = √20.

(ii) Find the equation of the circle centre P which passes through the point T. [5]

I know that a] will give D (-1, 4) and a radius of 3

But I have difficulty finding b and c. Can someone please help? I am having a lot of trouble with this and really need a bit of guidance.

Any help is appreciated