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

Let a circle $C_1 \equiv x^2 + y^2 - 4x + 6y + 1 = 0$ and circle $C_2$ be such that its centre is the image of the centre of $C_1$ about the $x$-axis and the radius of $C_2$ is equal to the radius of $C_1$. Then,the area of $C_1$ which is not common with $C_2$ is:

Let a circle $C$ in the complex plane pass through the points $z_{1}=3+4i$,$z_{2}=4+3i$,and $z_{3}=5i$. If $z(\neq z_{1})$ is a point on $C$ such that the line through $z$ and $z_{1}$ is perpendicular to the line through $z_{2}$ and $z_{3}$,then $\arg(z)$ is equal to

If $A\left(\frac{\pi}{3}\right)$ and $B\left(\frac{\pi}{6}\right)$ are points on a circle represented in parametric form with center $(0,0)$ and radius $12$,then the length of the chord $AB$ is:

Let $S$ be the circle in the $XY$-plane which touches the $X$-axis at point $A$,the $Y$-axis at point $B$,and the unit circle $x^2+y^2=1$ at point $C$ externally. If $O$ denotes the origin,then the angle $\angle OCA$ equals:

The triangle of maximum area inscribed in a circle is -