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1

### 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.

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

### 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 $$C_1$$.

solve it
3

### 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.)

solve it
4

### IIT-JEE 1996

Subjective
Find the intervals of value of a for which the line y + x = 0 bisects two chords drawn from a point $$\left( {{{1\, + \,\sqrt 2 a} \over 2},\,{{1\, - \,\sqrt 2 a} \over 2}} \right)$$ to the circle $$\,\,2{x^2}\, + \,2{y^2} - (\,1\, + \sqrt 2 a)\,x - (1 - \sqrt 2 a)\,y = 0$$.

$$a\, \in \,]\, - \infty ,\,\, - \,2\,[U]\,\,2,\,\,\infty \,[$$

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