1

IIT-JEE 2001

Subjective
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.

Answer

ellipse
2

IIT-JEE 1999

Subjective
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.

Answer


$${(x - y)^2} + \,{y^2} = {3^2}\,\,\,and\,\,{\left( {x + \,{4 \over 3}} \right)^2} + \,{y^2} = \,{\left( {{1 \over 3}} \right)^2};$$
$$y = \pm \,{5 \over {\sqrt {39} \,}}\left( {x + {4 \over 5}} \right)$$
3

IIT-JEE 1998

Subjective
$$C_1$$ and $$C_2$$ are two concentric circles, the radius of $$C_2$$ being twice that of $$C_1$$. From a point P on $$C_2$$, tangents PA and PB are drawn to $$C_1$$. Prove that the centroid of the triangle PAB lies on $$C_1$$.

Answer

solve it
4

IIT-JEE 1997

Subjective
Let C be any circle with centre $$\,\left( {0\, , \sqrt {2} } \right)$$. Prove that at the most two rational points can to there on C. (A rational point is a point both of whose coordinates are rational numbers.)

Answer

solve it

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