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1

IIT-JEE 2005

Subjective
Circles with radii 3, 4 and 5 touch each other externally. It P is the point of intersection of tangents to these circles at their points of contact, find the distance of P from the points of contact.

Answer

$$\sqrt 5 $$
2

IIT-JEE 2004

Subjective
Find the equation of circle touching the line 2x + 3y + 1 = 0 at (1, -1) and cutting orthogonally the circle having line segment joining (0, 3) and (- 2, -1) as diameter.

Answer

$$2{x^2}\, + 2\,{y^2} - 10x\, - 5y + 1\, = 0$$
3

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
4

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

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

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