1
IIT-JEE 2001 Screening
+2
-0.5
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
$$\sqrt {3y} = - \left( {3x + 1} \right)$$
2
IIT-JEE 2000 Screening
+2
-0.5
If $$x + y = k$$ is normal to $${y^2} = 12x,$$ then $$k$$ is
A
$$3$$
B
$$9$$
C
$$-9$$
D
$$-3$$
3
IIT-JEE 2000 Screening
+2
-0.5
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
$$1/4$$
4
IIT-JEE 1999
+2
-0.5
Let $$P$$ $$\left( {a\,\sec \,\theta ,\,\,b\,\tan \theta } \right)$$ and $$Q$$ $$\left( {a\,\sec \,\,\phi ,\,\,b\,\tan \,\phi } \right)$$, where $$\theta + \phi = \pi /2,$$, be two points on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$.

If $$(h, k)$$ is the point of intersection of the normals at $$P$$ and $$Q$$, then $$k$$ is equal to

A
$${{{a^2} + {b^2}} \over a}$$
B
$$- \left( {{{{a^2} + {b^2}} \over a}} \right)$$
C
$${{{a^2} + {b^2}} \over b}$$
D
$$- \left( {{{{a^2} + {b^2}} \over b}} \right)$$
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