The equation of the chord of contact,if the tangents are drawn from the point $(5, -3)$ to the circle $x^2 + y^2 = 10$,is

The equation of the transverse common tangent of the circles $x^2+y^2-6x-8y+9=0$ and $x^2+y^2+2x-2y+1=0$ 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

Given that $a > 2b > 0$ and that the line $y = mx - b \sqrt{1 + m^2}$ is a common tangent to the circles $x^2 + y^2 = b^2$ and $(x - a)^2 + y^2 = b^2$. Then the positive value of $m$ is

The equation of the pair of tangents drawn from the point $(6, -5)$ to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$ is:

The radius of the circle,having centre at $(2, 1)$ and one of its chords as a diameter of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$,is