1
IIT-JEE 2003
Subjective
+2
-0
For the circle $${x^2}\, + \,{y^2} = {r^2}$$, find the value of r for which the area enclosed by the tangents drawn from the point P (6, 8) to the circle and the chord of contact is maximum.
2
IIT-JEE 2001
Subjective
+5
-0
Let $$C_1$$ and $$C_2$$ be two circles with $$C_2$$ lying inside $$C_1$$. A circle C lying inside $$C_1$$ touches $$C_1$$ internally and $$C_2$$ externally. Identify the locus of the centre of C.
3
IIT-JEE 2001
Subjective
+5
-0
Let $$\,2{x^2}\, + \,{y^2} - \,3xy = 0$$ be the equation of a pair of tangents drawn from the origin O to a circle of radius 3 with centre in the first quadrant. If A is one of the points of contact, find the length of OA.
4
IIT-JEE 1999
Subjective
+10
-0
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.
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