1
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
$$\sqrt {{3 \over 2}} + 1$$
2
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
3
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
$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$
4
IIT-JEE 2007
+4
-1
Consider the circle $${x^2} + {y^2} = 9$$ and the parabola $${y^2} = 8x$$. They intersect at $$P$$ and $$Q$$ in the first and the fourth quadrants, respectively. Tangent to the circle at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$R$$ and tangents to the parabola at $$P$$ and $$Q$$ intersect the $$x$$-axis at $$S$$.

The ratio of the areas of the triangles $$PQS$$ and $$PQR$$ is

A
$$1:\sqrt 2$$
B
$$1:2$$
C
$$1:4$$
D
$$1:8$$
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