I really need some help on this problem:
1. The line x-2y=-4 is tangent to a circle at (0,2). The line y=2x-7 is tangent to the same circle at (3,-1). Find the center of the circle.
*If the equation of the circle is x^2 + y^2 = r^2 and the equation of the tangent line is y=mx+b, show that-
(a) r^2(1+m^2)= b^2
hint: the quadratic equation x^2 + (mx+b)^2 has exactly one solution
(b) the point of tangency is (-r^2 * m/b, r^2/b)
(c) the tangent line is perpendicular to the line containing the center of the circle and the point of tangency