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1

IIT-JEE 2004 Screening

The angle between the tangents drawn from the point $$(1, 4)$$ to the parabola $${y^2} = 4x$$ is
A
$$\pi /6$$
B
$$\pi /4$$
C
$$\pi /3$$
D
$$\pi /2$$
2

IIT-JEE 2003 Screening

The focal chord to $${y^2} = 16x$$ is tangent to $${\left( {x - 6} \right)^2} + {y^2} = 2,$$ then the possible values of the slope of the chord, are
A
$$\left\{ { - 1,\,1} \right\}$$
B
$$\left\{ { - 2,\,2} \right\}$$
C
$$\left\{ { - 2,\,-1/2} \right\}$$
D
$$\left\{ { 2,\,-1/2} \right\}$$
3

IIT-JEE 2003 Screening

For hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$ which of the following remains constant with change in $$'\alpha '$$
A
abscissae of vertices
B
abscissae of foci
C
eccentricity
D
directrix
4

IIT-JEE 2003 Screening

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1,$$ is
A
$$27/4$$ sq. units
B
$$9$$ sq. units
C
$$27/2$$ sq. units
D
$$27$$ sq. units

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