The two circles ${x^2} + {y^2} - 2x - 3 = 0$ and ${x^2} + {y^2} - 4x - 6y - 8 = 0$ are such that
They touch each other
They intersect each other
One lies inside the other
None of these
The equation of the image of the circle ${x^2} + {y^2} + 16x - 24y + 183 = 0$ by the line mirror $4x + 7y + 13 = 0$ is
If the two circles $2{x^2} + 2{y^2} - 3x + 6y + k = 0$ and ${x^2} + {y^2} - 4x + 10y + 16 = 0$ cut orthogonally, then the value of $k$ is
The range of values of $'a'$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi }{2} < \theta < \pi$ is :
Two given circles ${x^2} + {y^2} + ax + by + c = 0$ and ${x^2} + {y^2} + dx + ey + f = 0$ will intersect each other orthogonally, only when
The number of common tangents to two circles ${x^2} + {y^2} = 4$ and ${x^2} - {y^2} - 8x + 12 = 0$ is