Refer to Problem 65. The line x − 2y + 4 = 0 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.

Data from problem 65

If the equation of a circle is x² + y² = r² and the equation of a tangent line is y = mx + b, show that:

(a) r² (1 + m²) = b² .The quadratic equation x² + (mx + b)² = r² has exactly one solution.

(b) The point of tangency is

(c) The tangent line is perpendicular to the line containing the center of the circle and the point of tangency.

r -rm 2 b b