## Find the number of common tangents to the circles \(x^2 + y^2\) = 1 and \(x^2 + y^2 – 2x – 6y + 6\) = 0.

Solution : Let \(C_1\) be the center of circle \(x^2 + y^2\) = 1 i.e. \(C_1\) = (0, 0) And \(C_2\) be the center of circle \(x^2 + y^2 – 2x – 6y + 6\) = 0 i.e. \(C_2\) = (1, 3) Let \(r_1\) be the radius of first circle and \(r_2\) be the radius …