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1

### IIT-JEE 2002 Screening

If $$a > 2b > 0$$ then the positive value of $$m$$ for which $$y = mx - b\sqrt {1 + {m^2}}$$ is a common tangent to $${x^2} + {y^2} = {b^2}$$ and $${\left( {x - a} \right)^2} + {y^2} = {b^2}$$ is
A
$${{2b} \over {\sqrt {{a^2} - 4{b^2}} }}$$
B
$${{\sqrt {{a^2} - 4{b^2}} } \over {2b}}$$
C
$${{2b} \over {a - 2b}}$$
D
$${{b} \over {a - 2b}}$$
2

### IIT-JEE 2001 Screening

The equation of the common tangent touching the circle $${\left( {x - 3} \right)^2} + {y^2} = 9$$ and the parabola $${y^2} = 4x$$ above the $$x$$-axis is
A
$$\sqrt {3y} = 3x + 1$$
B
$$\sqrt {3y} = - \left( {x + 3} \right)$$
C
$$\sqrt {3y} = x + 3$$
D
$$\sqrt {3y} = - \left( {3x + 1} \right)$$
3

### IIT-JEE 2001 Screening

The equation of the directrix of the parabola $${y^2} + 4y + 4x + 2 = 0$$
A
$$x = - 1$$
B
$$x = 1$$
C
$$x = - 3/2$$
D
$$x = 3/2$$
4

### IIT-JEE 2000 Screening

If the line $$x - 1 = 0$$ is the directrix of the parabola $${y^2} - kx + 8 = 0,$$ then one of the values of $$k$$ is
A
$$1/8$$
B
$$8$$
C
$$4$$
D
$$1/4$$

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