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 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 :

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

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

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