Which of the following lines is a diameter of the circle $x^2 + y^2 - 6x - 8y - 9 = 0$?

If in two circles,arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre,find the ratio of their radii.

If the diameter of the circle $2(x^2 + y^2) + 3x + 4y - 1 = 0$ is $y = 2x + k$,then $k = \dots$

If a circle with centre at $(-1, 1)$ touches the line $x + 2y + 4 = 0$,then the coordinates of the point of contact are:

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

If the length of the chord $2x + 3y + k = 0$ of the circle $x^2 + y^2 - 2x + 4y - 11 = 0$ is $2\sqrt{3}$,then the sum of all possible values of $k$ is