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1

### IIT-JEE 2006

MCQ (Single Correct Answer)
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.

A line L' through A is drawn parallel to BD. Point S moves such that its distances from the BD and the vertex A are equal. If locus of S cuts L' at $$T_2$$ and $$T_3$$ and AC at $$T_1$$, then area of $$\Delta \,{T_1}\,{T_2}\,{T_3}$$ is

A
$${1 \over 2}\,sq.\,units$$
B
$${2 \over 3}\,sq.\,units$$
C
1 sq. units
D
2 sq.units
2

### IIT-JEE 2006

MCQ (Single Correct Answer)
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
3

### IIT-JEE 2005 Screening

MCQ (Single Correct Answer)
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
$$\{ (x,\,y):\,\,{x^2} = \,4y\} \, \cup \,\{ (0,\,\,y):\,\,y \le \,0\,\}$$
4

### IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
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

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