IIT-JEE 2009 Paper 1 Offline | Conic Sections Question 62 | Mathematics

1

IIT-JEE 2009 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-0

Match the conics in Column I with the statements/expressions in Column II :

	Column I		Column II
(A)	Circle	(P)	The locus of the point ($$h,k$$) for which the line $$hx+ky=1$$ touches the circle $$x^2+y^2=4$$.
(B)	Parabola	(Q)	Points z in the complex plane satisfying $$\|z+2\|-\|z-2\|=\pm3$$.
(C)	Ellipse	(R)	Points of the conic have parametric representation $$x = \sqrt 3 \left( {{{1 - {t^2}} \over {1 + {t^2}}}} \right),y = {{2t} \over {1 + {t^2}}}$$
(D)	Hyperbola	(S)	The eccentricity of the conic lies in the interval $$1 \le x \le \infty $$.
		(T)	Points z in the complex plane satisfying $${\mathop{\rm Re}\nolimits} {(z + 1)^2} = \|z{\|^2} + 1$$.

A

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(R); (D)$$\to$$(R), (S)

B

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(R); (D)$$\to$$(Q), (S)

C

(A)$$\to$$(P); (B)$$\to$$(S), (T); (C)$$\to$$(S); (D)$$\to$$(R), (S)

D

(A)$$\to$$(P); (B)$$\to$$(P), (T); (C)$$\to$$(R); (D)$$\to$$(Q), (S)

2

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

Consider a branch of the hyperbola $$${x^2} - 2{y^2} - 2\sqrt 2 x - 4\sqrt 2 y - 6 = 0$$$

with vertex at the point $$A$$. Let $$B$$ be one of the end points of its latus rectum. If $$C$$ is the focus of the hyperbola nearest to the point $$A$$, then the area of the triangle $$ABC$$ is

A

$$1 - \sqrt {{2 \over 3}} $$

B

$$\sqrt {{3 \over 2}} - 1$$

C

$$1 + \sqrt {{2 \over 3}} $$

D

$$\sqrt {{3 \over 2}} + 1$$

3

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

Consider the two curves $${C_1}:{y^2} = 4x,\,{C_2}:{x^2} + {y^2} - 6x + 1 = 0$$. Then,

A

$${C_1}$$ and $${C_2}$$ touch each other only at one point.

B

$${C_1}$$ and $${C_2}$$ touch each other exactly at two points

C

$${C_1}$$ and $${C_2}$$ intersect (but do not touch ) at exactly two points

D

$${C_1}$$ and $${C_2}$$ neither intersect nor touch each other

4

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

A hyperbola, having the transverse axis of length $$2\sin \theta ,$$ is confocal with the ellipse $$3{x^2} + 4{y^2} = 12.$$ Then its equation is

A

$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$

B

$${x^2}\cos e{c^2}\theta - {y^2}{\sec ^2}\theta = 1$$

C

$${x^2}{\sin ^2}\theta - {y^2}co{s^2}\theta = 1$$

D

$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$