1
IIT-JEE 2009 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-1

The locus of the orthocentre of the triangle formed by the lines

$$(1 + p)x - py + p(1 + p) = 0, $$

$$(1 + q)x - qy + q(1 + q) = 0$$

and $$y = 0$$, where $$p \ne q$$, is :

A
a hyperbola.
B
a parabola.
C
an ellipse.
D
a straight line.
2
IIT-JEE 2007
MCQ (Single Correct Answer)
+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
$$1:8$$
3
IIT-JEE 2007
MCQ (Single Correct Answer)
+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 radius of the circumcircle of the triangle $$PRS$$ is

A
$$5$$
B
$$3\sqrt 3 $$
C
$$3\sqrt 2 $$
D
$$2\sqrt 3 $$
4
IIT-JEE 2007
MCQ (Single Correct Answer)
+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 radius of the incircle of the triangle $$PQR$$ is

A
$$4$$
B
$$3$$
C
$${8 \over 3}$$
D
$$2$$
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