1

IIT-JEE 2007

MCQ (Single Correct Answer)
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
$$1:8$$
2

IIT-JEE 2007

MCQ (Single Correct Answer)
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
$${x^2}{\cos ^2}\theta - {y^2}{\sin ^2}\theta = 1$$
3

IIT-JEE 2006

MCQ (Single Correct Answer)
Match the following : $$(3, 0)$$ is the pt. from which three normals are drawn to the parabola $${y^2} = 4x$$ which meet the parabola in the points $$P, Q $$ and $$R$$. Then

Column $${\rm I}$$
(A) Area of $$\Delta PQR$$
(B) Radius of circumcircle of $$\Delta PQR$$
(C) Centroid of $$\Delta PQR$$
(D) Circumcentre of $$\Delta PQR$$

Column $${\rm I}$$$${\rm I}$$
(p) $$2$$
(q) $$5/2$$
(r) $$(5/2, 0)$$
(s) $$(2/3, 0)$$

A
$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( s \right),\left( D \right) - \left( r \right)$$
B
$$\left( A \right) - \left( p \right),\left( B \right) - \left( q \right),\left( C \right) - \left( r \right),\left( D \right) - \left( s \right)$$
C
$$\left( A \right) - \left( s \right),\left( B \right) - \left( r \right),\left( C \right) - \left( p \right),\left( D \right) - \left( q \right)$$
D
$$\left( A \right) - \left( r \right),\left( B \right) - \left( s \right),\left( C \right) - \left( q \right),\left( D \right) - \left( p \right)$$
4

IIT-JEE 2006

MCQ (Single Correct Answer)
The axis of a parabola is along the line $$y = x$$ and the distances of its vertex and focus from origin are $$\sqrt 2 $$ and $$2\sqrt 2 $$ respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
A
$${\left( {x + y} \right)^2} = \left( {x - y - 2} \right)$$
B
$${\left( {x - y} \right)^2} = \left( {x + y - 2} \right)$$
C
$${\left( {x - y} \right)^2} = 4\left( {x + y - 2} \right)$$
D
$${\left( {x - y} \right)^2} = 8\left( {x + y - 2} \right)$$

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