Let be two tangents drawn from on the circle

MATHEMATICS · Subjective · ISC · Mathematics · Coordinate Geometry · Coordinate Geometry

Problem

Let

T_1, T_2

be two tangents drawn from

(-2, 0)

on the circle

C: x^2 + y^2 = 1

. Determine the circles touching

C

and having

T_1, T_2

as their pair of tangents. Further, find the equations of all possible common tangents to these circles when taken two at a time.