The number of common tangents to two circles ${x^2} + {y^2} = 4$ and ${x^2} - {y^2} - 8x + 12 = 0$ is
$1$
$2$
$3$
$4$
The distance from the centre of the circle $x^2 + y^2 = 2x$ to the straight line passing through the points of intersection of the two circles $x^2 + y^2 + 5x -8y + 1 =0$ and $x^2 + y^2-3x + 7y -25 = 0$ is-
Three circles of radii $a, b, c\, ( a < b < c )$ touch each other externally. If they have $x -$ axis as a common tangent, then
The point $(2, 3)$ is a limiting point of a coaxial system of circles of which ${x^2} + {y^2} = 9$ is a member. The co-ordinates of the other limiting point is given by
The gradient of the radical axis of the circles ${x^2} + {y^2} - 3x - 4y + 5 = 0$ and $3{x^2} + 3{y^2} - 7x + 8y + 11 = 0$ is
The number of common tangents to the circles ${x^2} + {y^2} - 4x - 6y - 12 = 0$ and ${x^2} + {y^2} + 6x + 18y + 26 = 0$ is