Circle Diagram - http://i39.tinypic.com/33z48yq.png

1. The diagram shows a circle with centre (2,1) and radius 5.

a) Show that the equation of the circle may be written as:

x^2 + y^2 - 4x - 2y - 20 = 0

b) Find the coordinates of the Points P and Q where the circle cuts the y-axis. Leave your answers in the form a(+ or -) sqrt [b].

c) Verify the point A (5,-3) lies on the circle.

Show that the tangent to the circle at A has equation 4y = 3x - 27.

Thanks!