1

### 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.

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

### 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.

5
3

### 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.

$$3\,\left( {3\, + \sqrt {10} } \right)$$
4

### 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.

ellipse

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