If the circles $x^2+y^2-6x-8y-12=0$ and $x^2+y^2-4x+6y+k=0$ are orthogonal to each other,then the value of $k$ is:

The equation of the circle passing through the origin and cutting the circles $x^2+y^2+6x-15=0$ and $x^2+y^2-8y-10=0$ orthogonally is

If two circles touch at $(0,0)$ externally,then their radical axis is

From which point are the lengths of the tangents drawn to the circles $x^{2} + y^{2} - 8x + 40 = 0$,$5x^{2} + 5y^{2} - 25x + 80 = 0$,and $x^{2} + y^{2} - 8x + 16y + 160 = 0$ equal?

If the angle between the circles $x^2+y^2-4x-6y-3=0$ and $x^2+y^2+8x-4y+\lambda=0$ is $60^{\circ}$,then a value of $\lambda$ is

The locus of the centres of the circles which touch externally the circles $x^2 + y^2 = a^2$ and $x^2 + y^2 - 4ax = 0$ will be