1

### 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
$$\left\{ { 2,\,-1/2} \right\}$$
2

### 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
3

### 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
4

### IIT-JEE 2002 Screening

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$ is another parabola with directrix
A
$$x = -a$$
B
$$x = -a/2$$
C
$$x = 0$$
D
$$x = a/2$$

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