The equation of the circle which intersects circles ${x^2} + {y^2} + x + 2y + 3 = 0$, ${x^2} + {y^2} + 2x + 4y + 5 = 0$and ${x^2} + {y^2} - 7x - 8y - 9 = 0$ at right angle, will be
${x^2} + {y^2} - 4x - 4y - 3 = 0$
$3({x^2} + {y^2}) + 4x - 4y - 3 = 0$
${x^2} + {y^2} + 4x + 4y - 3 = 0$
$3({x^2} + {y^2}) + 4(x + y) - 3 = 0$
If ${x^2} + {y^2} + px + 3y - 5 = 0$ and ${x^2} + {y^2} + 5x$ $ + py + 7 = 0$ cut orthogonally, then $p$ is
Two circle ${x^2} + {y^2} = ax$ and ${x^2} + {y^2} = {c^2}$ touch each other if
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
For the two circles $x^2 + y^2 = 16$ and $x^2 + y^2 -2y = 0,$ there is/are
The number of common tangent$(s)$ to the circles $x^2 + y^2 + 2x + 8y - 23 = 0$ and $x^2 + y^2 - 4x - 10y + 19 = 0$ is :