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 P is any point of $${C_1}$$ and Q is another point on $${C_2}$$, then

$${{P{A^2}\, + \,P{B^2}\, + P{C^2}\, + P{D^2}} \over {Q{A^2} + \,Q{B^2}\, + Q{C^2}\, + Q{D^2}}}$$ is equal to
A
0.75
B
1.25
C
1
D
0.5
2

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.

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
3

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
4

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

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