1

### IIT-JEE 2012 Paper 1 Offline

The ellipse $${E_1}:{{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ is inscribed in a rectangle $$R$$ whose sides are parallel to the coordinate axes. Another ellipse $${E_2}$$ passing through the point $$(0, 4)$$ circumscribes the rectangle $$R$$. The eccentricity of the ellipse $${E_2}$$ is
A
$${{\sqrt 2 } \over 2}$$
B
$${{\sqrt 3 } \over 2}$$
C
$${{1 \over 2}}$$
D
$${{3 \over 4}}$$
2

### IIT-JEE 2011 Paper 2 Offline

Let $$P(6, 3)$$ be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at the point $$P$$ intersects the $$x$$-axis at $$(9, 0)$$, then the eccentricity of the hyperbola is
A
$$\sqrt {{5 \over 2}}$$
B
$$\sqrt {{3 \over 2}}$$
C
$${\sqrt 2 }$$
D
$${\sqrt 3 }$$
3

### IIT-JEE 2011 Paper 2 Offline

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
$${x^2} = 2y$$
4

### IIT-JEE 2010 Paper 2 Offline

Tangents are drawn from the point $$P(3, 4)$$ to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ touching the ellipse at points $$A$$ and $$B$$.

The orthocentre of the triangle $$PAB$$ is

A
$$\left( {5,{8 \over 7}} \right)$$
B
$$\left( {{7 \over 5},{{25} \over 8}} \right)$$
C
$$\left( {{11 \over 5},{{8} \over 5}} \right)$$
D
$$\left( {{8 \over 25},{{7} \over 5}} \right)$$

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