AIEEE 2005 | Circle Question 152 | Mathematics

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 :

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

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

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

$${(x\, - \,p)^2} = \,4\,qy$$

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 :

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

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

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

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

AIEEE 2004

MCQ (Single Correct Answer)

-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 :

$$2ax\, - 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$

$$2ax\, + 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$$

$$2ax\, - 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$

$$2ax\, + 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$$

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