1
AIEEE 2005
+4
-1
A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is
A
an ellipse
B
a circle
C
a hyperbola
D
a parabola
2
AIEEE 2005
+4
-1
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = {p^2}$$ orthogonally, then the equation of the locus of its centre is
A
$${x^2}\, + \,{y^2} - \,3ax\, - \,4\,by\,\, + \,({a^2}\, + \,{b^2} - {p^2}) = 0$$
B
$$2ax\, + \,\,2\,by\,\, - \,({a^2}\, - \,{b^2} + {p^2}) = 0$$
C
$${x^2}\, + \,{y^2} - \,2ax\, - \,\,3\,by\,\, + \,({a^2}\, - \,{b^2} - {p^2}) = 0$$
D
$$2ax\, + \,\,2\,by\,\, - \,({a^2}\, + \,{b^2} + {p^2}) = 0$$
3
AIEEE 2005
+4
-1
If the circles $${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$$ and $${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0$$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for
A
exactly one value of a
B
no value of a
C
infinitely many values of a
D
exactly two values of a
4
AIEEE 2005
+4
-1
If the pair of lines $$a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then
A
$$3{a^2} - 10ab + 3{b^2} = 0$$
B
$$3{a^2} - 2ab + 3{b^2} = 0$$
C
$$3{a^2} + 10ab + 3{b^2} = 0$$
D
$$3{a^2} + 2ab + 3{b^2} = 0$$
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