1
AIEEE 2004
+4
-1
Intercept on the line y = x by the circle $${x^2}\, + \,{y^2} - 2x = 0$$ is AB. Equation of the circle on AB as a diameter is
A
$$\,{x^2}\, + \,{y^2} + \,x\, - \,y\,\, = 0$$
B
$$\,{x^2}\, + \,{y^2} - \,x\, + \,y\,\, = 0$$
C
$$\,{x^2}\, + \,{y^2} + \,x\, + \,y\,\, = 0$$
D
$$\,{x^2}\, + \,{y^2} - \,x\, - \,y\,\, = 0$$
2
AIEEE 2003
+4
-1
If the two circles $${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$$ and $$\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0$$ intersect in two distinct point, then
A
$$r > 2$$
B
$$2 < r < 8$$
C
$$r < 2$$
D
$$r = 2.$$
3
AIEEE 2003
+4
-1
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is
A
$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,62$$
B
$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,62$$
C
$${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,47$$
D
$${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,47$$
4
AIEEE 2002
+4
-1
If the chord y = mx + 1 of the circle $${x^2}\, + \,{y^2} = 1$$ subtends an angle of measure $${45^ \circ }$$ at the major segment of the circle then value of m is
A
$$2\, \pm \,\sqrt 2 \,\,$$
B
$$- \,2\, \pm \,\sqrt 2 \,$$
C
$$- 1\, \pm \,\sqrt 2 \,\,$$
D
none of these
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