1
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
2
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
$$3{a^2} + 2ab + 3{b^2} = 0$$
3
AIEEE 2004
+4
-1
If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $$10\,\pi$$, then the equation of the circle is :
A
$${x^2}\, + \,{y^2} + \,2x\, - \,2y - \,23\,\, = 0$$
B
$${x^2}\, + \,{y^2} - \,2x\, - \,2y - \,23\,\, = 0$$
C
$${x^2}\, + \,{y^2} + \,2x\, + \,2y - \,23\,\, = 0$$
D
$${x^2}\, + \,{y^2} - \,2x\, + \,2y - \,23\,\, = 0$$
4
AIEEE 2004
+4
-1
If a circle passes through the point (a, b) and cuts the circle $${x^2}\, + \,{y^2} = 4$$ orthogonally, then the locus of its centre is :
A
$$2ax\, - 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$
B
$$2ax\, + 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$
C
$$2ax\, - 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$
D
$$2ax\, + 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$
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