1
IIT-JEE 2009 Paper 1 Offline
+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
+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
+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
+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
$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$
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