1
IIT-JEE 2003 Screening
+2
-0.5
For hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ which of the following remains constant with change in $$'\alpha '$$
A
abscissae of vertices
B
abscissae of foci
C
eccentricity
D
directrix
2
IIT-JEE 2003 Screening
+2
-0.5
The focal chord to $${y^2} = 16x$$ is tangent to $${\left( {x - 6} \right)^2} + {y^2} = 2,$$ then the possible values of the slope of the chord, are
A
$$\left\{ { - 1,\,1} \right\}$$
B
$$\left\{ { - 2,\,2} \right\}$$
C
$$\left\{ { - 2,\,-1/2} \right\}$$
D
$$\left\{ { 2,\,-1/2} \right\}$$
3
IIT-JEE 2002 Screening
+2
-0.5
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 2002 Screening
+2
-0.5
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
$$x = a/2$$
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