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1

IIT-JEE 2003

Subjective
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.

Answer

5
2

IIT-JEE 2001

Subjective
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.

Answer

$$3\,\left( {3\, + \sqrt {10} } \right)$$
3

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
4

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


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

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