AIEEE 2005 | Circle Question 150 | Mathematics

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 2005

MCQ (Single Correct Answer)

-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 :

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

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 :

$${x^2}\, + \,{y^2} + \,2x\, - \,2y - \,23\,\, = 0$$

$${x^2}\, + \,{y^2} - \,2x\, - \,2y - \,23\,\, = 0$$

$${x^2}\, + \,{y^2} + \,2x\, + \,2y - \,23\,\, = 0$$

$${x^2}\, + \,{y^2} - \,2x\, + \,2y - \,23\,\, = 0$$