The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

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 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 one end of the diameter of $x^2+y^2-2x-6y-15=0$ is $(4,1)$,then the coordinates of the other end are:

In a triangle,two vertices are $(2, 3)$ and $(4, 0)$,and its circumcentre is $(2, z)$ for some real number $z$. The circumradius is

If the angle between the circles $x^2+y^2+4x-5=0$ and $x^2+y^2+2\lambda y-4=0$ is $\frac{\pi}{3}$,then $\lambda=$