1

JEE Advanced 2014 Paper 2 Offline

The common tangents to the circle $${x^2} + {y^2} = 2$$ and the parabola $${y^2} = 8x$$ touch the circle at the points $$P, Q$$ and the parabola at the points $$R$$, $$S$$. Then the area of the quadrilateral $$PQRS$$ is
A
$$3$$
B
$$6$$
C
$$9$$
D
$$15$$
2

JEE Advanced 2013 Paper 2 Offline

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
$${-2 \over 3}\sqrt 5$$
3

JEE Advanced 2013 Paper 2 Offline

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 $$y=2x+a$$, $$a>0$$.

Length of chord $$PQ$$ is

A
$$7a$$
B
$$5a$$
C
$$2a$$
D
$$3a$$
4

JEE Advanced 2013 Paper 2 Offline

A line $$L:y=mx+3$$ meets $$y$$-axis at $$(E, 3)$$ and the are of the parabola $${y^2} = 16x,$$ $$0 \le y \le 6$$ at the point $$F\left( {{x_0},{y_0}} \right)$$. The tangent to the parabola at $$F\left( {{x_0},{y_0}} \right)$$ intersects the $$y$$-axis at $$G\left( {0,{y_1}} \right)$$. The slope $$m$$ of the line $$L$$ is chosen such that the area of the triangle $$EFG$$ has a local maximum.

Match List $$I$$ with List $$II$$ and select the correct answer using the code given below the lists:

List $$I$$
P.$$\,\,\,m =$$
Q.$$\,\,\,$$Maximum area of $$\Delta EFG$$ is
R.$$\,\,\,$$ $${y_0} =$$
S.$$\,\,\,$$ $${y_1} =$$

List $$II$$
1.$$\,\,\,$$ $${1 \over 2}$$
2.$$\,\,\,$$ $$4$$
3.$$\,\,\,$$ $$2$$
4.$$\,\,\,$$ $$1$$

A
$$P = 4,Q = 1,R = 2,S = 3$$
B
$$P = 3,Q = 4,R = 1,S = 2$$
C
$$P = 1,Q = 3,R = 2,S = 4$$
D
$$P = 1,Q = 3,R = 4,S = 2$$

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