The number of common tangents to the circles $x^2+y^2-4x-2y+k=0$ and $x^2+y^2-6x-4y+l=0$,having radii $2$ and $3$ respectively,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 the chord $x+y=1$ of the circle $x^2+y^2=a^2$ subtends a right angle at the origin,then $a=$

If the ratio of the lengths of the tangents drawn from the point $(1, 2)$ to the circles $x^2 + y^2 + x + y - 4 = 0$ and $3x^2 + 3y^2 - x - y + k = 0$ is $4 : 3$,then $k = \dots$

If the four distinct points $(4,6), (-1,5), (0,0)$ and $(k, 3k)$ lie on a circle of radius $r$,then $10k + r^2$ is equal to

Given two circles $x^2+y^2+8x-6y-24=0$ and $x^2+y^2-4x+10y+20=0$. Then they are