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1

### IIT-JEE 2006

ABCD is a square of side length 2 units. $$C_1$$ is the circle touching all the sides of the square ABCD and $$C_2$$ is the circumcircle of square ABCD. L is a fixed line in the same plane and R is a fixed point.

If a circle is such that it touches the line L and the circle $$C_1$$ externally, such that both the circles are on the same side of the line, then the locus of centre of the circle is

A
ellipse
B
hyper bola
C
parabola
D
pair of straight line
2

### IIT-JEE 2005 Screening

A circle is given by $${x^2}\, + \,{(y\, - \,1\,)^2}\, = \,1$$, another circle C touches it externally and also the x-axis, then thelocus of its centre is
A
$$\{ (x,\,y):\,\,{x^2} = \,4y\} \, \cup \,\{ (x,\,y):\,\,y \le \,0\,\}$$
B
$$\{ (x,\,y):\,\,{x^2} + \,{(y\, - \,1)^2}\, = \,4\} \, \cup \,\{ (x,\,\,y):\,\,y \le \,0\,\}$$
C
$$\{ (x,\,y):\,\,{x^2} = \,y\} \, \cup \,\{ (0,\,\,y):\,\,y \le \,0\,\}$$
D
$$\{ (x,\,y):\,\,{x^2} = \,4y\} \, \cup \,\{ (0,\,\,y):\,\,y \le \,0\,\}$$
3

### IIT-JEE 2004 Screening

If one of the diameters of the circle $${x^2} + {y^2} - 2x - 6y + 6 = 0$$ is a chord to the circle with centre (2, 1), then the radius of the circle is
A
$${\sqrt 3 }$$
B
$${\sqrt 2 }$$
C
3
D
2
4

### IIT-JEE 2003 Screening

The centre of circle inscibed in square formed by the lines $${x^2} - 8x + 12 = 0\,\,and\,{y^2} - 14y + 45 = 0$$, is
A
(4, 7)
B
(7, 4)
C
(9, 4)
D
(4, 9)

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