The number of common tangents to the circles ${x^2} + {y^2} = 1$and ${x^2} + {y^2} - 4x + 3 = 0$ is
$1$
$2$
$3$
$4$
If a circle passes through the point $(a , b) \&$ cuts the circle $x^2 + y^2= K^2$ orthogonally, then the equation of the locus of its centre is :
The centre of the circle, which cuts orthogonally each of the three circles ${x^2} + {y^2} + 2x + 17y + 4 = 0,$ ${x^2} + {y^2} + 7x + 6y + 11 = 0,$ ${x^2} + {y^2} - x + 22y + 3 = 0$ is
One of the limit point of the coaxial system of circles containing ${x^2} + {y^2} - 6x - 6y + 4 = 0$, ${x^2} + {y^2} - 2x$ $ - 4y + 3 = 0$ is
If the curves, $x^{2}-6 x+y^{2}+8=0$ and $\mathrm{x}^{2}-8 \mathrm{y}+\mathrm{y}^{2}+16-\mathrm{k}=0,(\mathrm{k}>0)$ touch each other at a point, then the largest value of $\mathrm{k}$ is
The equation of the circle through the points of intersection of ${x^2} + {y^2} - 1 = 0$, ${x^2} + {y^2} - 2x - 4y + 1 = 0$ and touching the line $x + 2y = 0$, is