Refer to Problem 1. The line x − 2y + 4 = 0 is tangent to a circle at (0, 2). The line y =...

Refer to Problem 1. 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.

Problem 1

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. See the figure.