the problem solve it

the problem solve it
The tangent line to a circle may be defined as the line that intersects the circle in a single point,called the point of tangency.If the equation if the circle is
x^2 + y^2 = r^2 and the equation of the tangent line is y = mx + b,
a) show that r^2(1 + m^2) = b^2
b) the point of tangency is (-r^2m/b,r^2/b)
c) the tangent line is perpendicular to the line containing the center of the circle and the point of tangency.
HINT:The quadratic equation x^2 + (mx + b) ^2 = r^2 has exactly one solution.