1

### JEE Advanced 2014 Paper 2 Offline

Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a{s^2},2as} \right)$$ be distinct points on the parabola $${y^2} = 4ax$$. Suppose that $$PQ$$ is the focal chord and lines $$QR$$ and $$PK$$ are parallel, where $$K$$ is the point $$(2a,0)$$

If $$st=1$$, then the tangent at $$P$$ and the normal at $$S$$ to the parabola meet at a point whose ordinate is

A
$${{{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$$
B
$${{a{{\left( {{t^2} + 1} \right)}^2}} \over {2{t^3}}}$$
C
$${{a{{\left( {{t^2} + 1} \right)}^2}} \over {{t^3}}}$$
D
$${{a{{\left( {{t^2} + 2} \right)}^2}} \over {{t^3}}}$$
2

### JEE Advanced 2014 Paper 2 Offline

Let $$a, r, s, t$$ be nonzero real numbers. Let $$P\,\,\left( {a{t^2},2at} \right),\,\,Q,\,\,\,R\,\,\left( {a{r^2},2ar} \right)$$ and $$S\,\,\left( {a{s^2},2as} \right)$$ be distinct points on the parabola $${y^2} = 4ax$$. Suppose that $$PQ$$ is the focal chord and lines $$QR$$ and $$PK$$ are parallel, where $$K$$ is the point $$(2a,0)$$

The value of $$r$$ is

A
$$- {1 \over t}$$
B
$${{{t^2} + 1} \over t}$$
C
$${1 \over t}$$
D
$${{{t^2} - 1} \over t}$$
3

### 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
$$15$$
4

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

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