1
JEE Advanced 2013 Paper 2 Offline
MCQ (Single Correct Answer)
+4
-1
Let $$PQ$$ be a focal chord of the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$P$$ and $$Q$$ meet at a point lying on the line $$y=2x+a$$, $$a>0$$.

If chord $$PQ$$ subtends an angle $$\theta$$ at the vertex of $${y^2} = 4ax$$, then tan $$\theta =$$

A
$${2 \over 3}\sqrt 7$$
B
$${-2 \over 3}\sqrt 7$$
C
$${2 \over 3}\sqrt 5$$
D
$${-2 \over 3}\sqrt 5$$
2
IIT-JEE 2011 Paper 2 Offline
MCQ (Single Correct Answer)
+3
-0.75
Let $$(x, y)$$ be any point on the parabola $${y^2} = 4x$$. Let $$P$$ be the point that divides the line segment from $$(0, 0)$$ to $$(x, y)$$ in the ratio $$1 : 3$$. Then the locus of $$P$$ is
A
$${x^2} = y$$
B
$${y^2} = 2x$$
C
$${y^2} = x$$
D
$${x^2} = 2y$$
3
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.
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 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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