The centre of the smallest circle touching the circles $x^2 + y^2- 2y - 3 = 0$ and $x^2+ y^2 - 8x - 18y + 93 = 0$ is :
$(3 , 2)$
$(4 , 4)$
$(2 , 7)$
$(2 , 5)$
The point of contact of the given circles ${x^2} + {y^2} - 6x - 6y + 10 = 0$ and ${x^2} + {y^2} = 2$, is
The number of common tangents to the circles ${x^2} + {y^2} - x = 0,\,{x^2} + {y^2} + x = 0$ is
If the variable line $3 x+4 y=\alpha$ lies between the two circles $(x-1)^{2}+(y-1)^{2}=1$ and $(x-9)^{2}+(y-1)^{2}=4$ without intercepting a chord on either circle, then the sum of all the integral values of $\alpha$ is .... .
If the circles ${x^2} + {y^2} - 2ax + c = 0$ and ${x^2} + {y^2} + 2by + 2\lambda = 0$ intersect orthogonally, then the value of $\lambda $ is
If the circles of same radius a and centers at $(2, 3)$ and $(5, 6)$ cut orthogonally, then $a =$