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1

### IIT-JEE 2006

The axis of a parabola is along the line $$y = x$$ and the distances of its vertex and focus from origin are $$\sqrt 2$$ and $$2\sqrt 2$$ respectively. If vertex and focus both lie in the first quadrant, then the equation of the parabola is
A
$${\left( {x + y} \right)^2} = \left( {x - y - 2} \right)$$
B
$${\left( {x - y} \right)^2} = \left( {x + y - 2} \right)$$
C
$${\left( {x - y} \right)^2} = 4\left( {x + y - 2} \right)$$
D
$${\left( {x - y} \right)^2} = 8\left( {x + y - 2} \right)$$
2

### IIT-JEE 2005 Screening

Tangent to the curve $$y = {x^2} + 6$$ at a point $$(1, 7)$$ touches the circle $${x^2} + {y^2} + 16x + 12y + c = 0$$ at a point $$Q$$. Then the coordinates of $$Q$$ are
A
$$(-6, -11)$$
B
$$(-9, -13)$$
C
$$(-10, -15)$$
D
$$(-6, -7)$$
3

### IIT-JEE 2005 Screening

The minimum area of triangle formed by the tangent to the $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ and coordinate axes is
A
$$ab$$ sq. units
B
$${{{{a^2} + {b^2}} \over 2}}$$ sq. units
C
$${{{{\left( {a + b} \right)}^2}} \over 2}$$ sq. units
D
$${{{a^2} + ab + {b^2}} \over 3}$$ sq. units
4

### IIT-JEE 2004 Screening

If the line $$62x + \sqrt 6 y = 2$$ touches the hyperbola $${x^2} - 2{y^2} = 4$$, then the point of contact is
A
$$\left( { - 2,\,\sqrt 6 } \right)$$
B
$$\left( { - 5,\,2\sqrt 6 } \right)$$
C
$$\left( {{1 \over 2},{1 \over {\sqrt 6 }}} \right)$$
D
$$\left( {4, - \,\sqrt 6 } \right)$$

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