1
IIT-JEE 2011 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let the eccentricity of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ be reciprocal to that of the ellipse $${x^2} + 4{y^2} = 4$$. If the hyperbola passes through a focus of the ellipse, then
A
the equation of the hyperbola is $${{{x^2}} \over 3} - {{{y^2}} \over 2} = 1$$
B
a focus of the hyperbola is $$(2, 0)$$
C
theeccentricity of the hyperbola is $$\sqrt {{5 \over 3}}$$
D
The equation of the hyperbola is $${x^2} - 3{y^2} = 3$$
2
IIT-JEE 2011 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-1

Let L be a normal to the parabola y2 = 4x. If L passes through the point (9, 6), then L is given by

A
y $$-$$ x + 3 = 0
B
y + 3x $$-$$ 33 = 0
C
y + x $$-$$ 15 = 0
D
7 $$-$$ 2x + 12 = 0
3
IIT-JEE 2010 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$A$$ and $$B$$ be two distinct points on the parabola $${y^2} = 4x$$. If the axis of the parabola touches a circle of radius $$r$$ having $$AB$$ as its diameter, then the slope of the line joining $$A$$ and $$B$$ can be
A
$$- {1 \over r}$$
B
$${1 \over r}$$
C
$${2 \over r}$$
D
$$- {2 \over r}$$
4
IIT-JEE 2009 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a point $$P$$ on it meet its axis at points $$T$$ and $$N$$, respectively. The locus of the centroid of the triangle $$PTN$$ is a parabola whose
A
vertex is $$\left( {{{2a} \over 3},0} \right)$$
B
directrix is $$x=0$$
C
latus rectum is $${{{2a} \over 3}}$$
D
focus is $$(a, 0)$$
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