AIEEE 2005 | Circle Question 175 | 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 2005

MCQ (Single Correct Answer)

-1

Out of Syllabus

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 :

an ellipse

a circle

a hyperbola

a parabola

AIEEE 2005

MCQ (Single Correct Answer)

-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 :

$${x^2}\, + \,{y^2} - \,3ax\, - \,4\,by\,\, + \,({a^2}\, + \,{b^2} - {p^2}) = 0$$

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

$${x^2}\, + \,{y^2} - \,2ax\, - \,\,3\,by\,\, + \,({a^2}\, - \,{b^2} - {p^2}) = 0$$

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

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 :

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

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

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