Two circles centered at $(2,3)$ and $(4,5)$ intersect each other. If their radii are equal,then the equation of the common chord is

If the circle ${C_1}: {x^2} + {y^2} = 16$ intersects another circle ${C_2}$ of radius $5$ in such a manner that the common chord is of maximum length and has a slope equal to $\frac{3}{4}$,the coordinates of the centre of ${C_2}$ are

Chords of the curve $4x^2 + y^2 - x + 4y = 0$ which subtend a right angle at the origin pass through a fixed point whose coordinates are:

If the circle $S \equiv x^2+y^2-4=0$ intersects another circle $S^{\prime}=0$ of radius $\frac{5 \sqrt{2}}{2}$ in such a manner that the common chord is of maximum length with slope equal to $\frac{1}{4}$,then the centre of $S^{\prime}=0$ 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

Two circles centered at $(2,3)$ and $(5,6)$ intersect each other. If the radii are equal,the equation of the common chord is