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### IIT-JEE 1997

Fill in the Blanks
For each natural number k, let $${C_k}$$ denote the circle with radius k centimetres and centre at the origin. On the circle $${C_k}$$, a-particle moves k centimetres in the counter-clockwise direction. After completing its motion on $${C_k}$$, the particle moves to $${C_{k + 1}}$$ in the radial direction. The motion of the patticle continues in the manner. The particle starts at (1, 0). If the particle crosses the positive direction of the x-axis for the first time on the circle $${C_n}$$ then n = ..............

7
2

### IIT-JEE 1996

Fill in the Blanks
The intercept on the line y = x by the circle $${x^2} + {y^2} - 2x = 0$$ is AB. Equation of the circle with AB as a diameter is................................

$${x^2} + {y^2} - x - y = 0$$
3

### IIT-JEE 1993

Fill in the Blanks
The equation of the locus of the mid-points of the circle $$4{x^2} + 4{y^2} - 12x + 4y + 1 = 0$$ that subtend an angle of $$2\pi /3$$ at its centre is.................................

$$16{x^2} + 16{y^2} - 48x + 16y + 31 = 0$$
4

### IIT-JEE 1991

Fill in the Blanks
If a circle passes through the points of intersection of the coordinate axes with the lines $$\lambda \,x - y + 1 = 0$$ and x - 2y + 3 = 0, then the value of $$\lambda$$ = .........

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