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1

### IIT-JEE 2000 Screening

If the circles $${x^2}\, + \,{y^2}\, + \,\,2x\, + \,2\,k\,y\,\, + \,6\,\, = \,\,0,\,\,{x^2}\, + \,\,{y^2}\, + \,2ky\, + \,k\, = \,0$$ intersect orthogonally, then k is
A
2 or $$- {3 \over 2}$$
B
- 2 or $$- {3 \over 2}$$
C
2 or $${3 \over 2}$$
D
- 2 or $${3 \over 2}$$
2

### IIT-JEE 2000 Screening

The triangle PQR is inscribed in the circle $${x^2}\, + \,\,{y^2} = \,25$$. If Q and R have co-ordinates (3, 4) and ( - 4, 3) respectively, then $$\angle \,Q\,P\,R$$ is equal to
A
$${\pi \over 2}$$
B
$${\pi \over 3}$$
C
$${\pi \over 4}$$
D
$${\pi \over 6}$$
3

### IIT-JEE 1999

If two distinct chords, drawn from the point (p, q) on the circle $${x^2}\, + \,{y^2} = \,px\, + \,qy\,\,(\,where\,pq\, \ne \,0)$$ are bisected by the x - axis, then
A
$${p^2}\, = \,\,{q^2}$$
B
$$\,{p^2}\, = \,\,8\,{q^2}$$
C
$${p^2}\, < \,\,8\,{q^2}$$
D
$${p^2}\, > \,\,8\,{q^2}$$.
4

### IIT-JEE 1996

The angle between a pair of tangents drawn from a point P to the circle $${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,9\,{\sin ^2}\,\alpha \, + \,13\,{\cos ^2}\,\alpha \, = \,0$$ is $$2\,\alpha$$.
The equation of the locus of the point P is
A
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,4\, = \,0$$
B
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,9\,\, = \,0$$
C
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, - \,4\,\, = \,0$$
D
$${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\,\, + \,9\,\, = \,0$$

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