1

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is another parabola with directrix
A
$$x = -a$$
B
$$x = -a/2$$
C
$$x = 0$$
D
$$x = a/2$$
2

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
The equation of the common tangent to the curves $${y^2} = 8x$$ and $$xy = - 1$$ is
A
$$3y = 9x + 2$$
B
$$y = 2x + 1$$
C
$$2y = x + 8$$
D
$$y= x + 2$$
3

IIT-JEE 2002 Screening

MCQ (Single Correct Answer)
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
$${{b} \over {a - 2b}}$$
4

IIT-JEE 2001 Screening

MCQ (Single Correct Answer)
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
$$\sqrt {3y} = - \left( {3x + 1} \right)$$

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