JEE Advance - Mathematics (1999 - No. 29)
Let $${T_1}$$, $${T_2}$$ be two tangents drawn from (- 2, 0) onto 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.
The centers of the circles touching C and having T1, T2 as tangents lie on the lines y = ± (x + 2).
The radii of the circles touching C and having T1, T2 as tangents are 3 and 1/3.
The equations of the circles touching C and having T1, T2 as their pair of tangents are (x - 3)^2 + y^2 = 3^2 and (x + 4/3)^2 + y^2 = (1/3)^2.
The common tangents to these circles are y = ± (5/√39)(x + 4/5).
The points of tangency of T1 and T2 with circle C are (1,0) and (-1,0) respectively.
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