AIEEE 2005 | Circle Question 151 | Mathematics

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 :

exactly one value of a

no value of a

infinitely many values of a

exactly two values of a

AIEEE 2005

MCQ (Single Correct Answer)

-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 :

$$3{a^2} - 10ab + 3{b^2} = 0$$

$$3{a^2} - 2ab + 3{b^2} = 0$$

$$3{a^2} + 10ab + 3{b^2} = 0$$

$$3{a^2} + 2ab + 3{b^2} = 0$$

AIEEE 2004

MCQ (Single Correct Answer)

-1

Out of Syllabus

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :

$${(y\, - \,q)^2} = \,4\,px$$

$${(x\, - \,q)^2} = \,4\,py$$

$${(y\, - \,p)^2} = \,4\,qx$$