The length of the common chord of the circles $x^2 + y^2 + 2x + 3y + 1 = 0$ and $x^2 + y^2 + 4x + 3y + 2 = 0$ is

The length of the common chord of the circles $(x - a)^2 + y^2 = a^2$ and $x^2 + (y - b)^2 = b^2$ is

If a variable circle $S=0$ touches the line $y=x$ and passes through the point $(0,0)$,then the fixed point that lies on the common chord of the circles $x^2+y^2+6x+8y-7=0$ and $S=0$ is

If the line $x+y+1=0$ intersects the circle $x^2+y^2+x+3y=0$ at two points $A$ and $B$,then the centre of the circle which passes through the points $A, B$ and the point of intersection of the tangents drawn at $A$ and $B$ to the given circle is

If the common chord of the circles $x^2+y^2+4y=0$ and $x^2+y^2-4x-5=0$ is the diameter of the circle $S=0$,then the abscissa of the centre of the circle $S=0$ is

If the circle $S_1: x^2+y^2=16$ intersects another circle $S_2$ of radius $5$ units such that the common chord is of maximum length and has a slope of $\frac{3}{4}$,then the center of the circle $S_2$ is