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1

IIT-JEE 2012 Paper 1 Offline

MCQ (More than One Correct Answer)
Tangents are drawn to the hyperbola $${{{x^2}} \over 9} - {{{y^2}} \over 4} = 1,$$ parallel to the straight line $$2x - y = 1,$$ The points of contact of the tangents on the hyperbola are
A
$$\left( {{9 \over {2\sqrt 2 }},{1 \over {\sqrt 2 }}} \right)$$
B
$$\left( -{{9 \over {2\sqrt 2 }},-{1 \over {\sqrt 2 }}} \right)$$
C
$$\left( {3\sqrt 3 , - 2\sqrt 2 } \right)$$
D
$$\left( -{3\sqrt 3 , 2\sqrt 2 } \right)$$
2

IIT-JEE 2011 Paper 2 Offline

MCQ (More than One Correct Answer)

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

Explanation

The equation of normal is

y = mx $$-$$ 2m $$-$$ m3

As (9, 6) lies on it, 6 = 9m $$-$$ 2m $$-$$ m33 $$-$$ 7m + 6 = 0

The roots are m = 1, 2, $$-$$3. So the normal are

y = x $$-$$ 3, y = 2x $$-$$ 12, y = $$-$$3x + 33.

3

IIT-JEE 2011 Paper 2 Offline

MCQ (More than One Correct Answer)
Let $$L$$ be a normal to the parabola $${y^2} = 4x.$$ 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
$$y - 2x + 12 = 0$$
4

IIT-JEE 2011 Paper 1 Offline

MCQ (More than One Correct Answer)
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 $${x^2} - 3{y^2} = 3$$

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