AIEEE 2005 | Circle Question 176 | 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

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 :

$$\,{x^2}\, + \,{y^2} + \,x\, - \,y\,\, = 0$$

$$\,{x^2}\, + \,{y^2} - \,x\, + \,y\,\, = 0$$

$$\,{x^2}\, + \,{y^2} + \,x\, + \,y\,\, = 0$$

$$\,{x^2}\, + \,{y^2} - \,x\, - \,y\,\, = 0$$