hello im bit confused how to solve this

1.Show that the line y = mx + c touches the circle x^2 + y^2 = a^2 if c^2 = a^2(1+m^2)

2.The point (p,q) lies on the circle x^2 + y^2 = a^2.

Show that the equation of the tangent to the circle at (p,q) is px + qy = a^2

3. A circle passes through the points C (4,4) and D (10,2).

The line 2y = x + 4 is a tangent to the circle at C

Find the euqation of the circle

thanks