The radical axis of the pair of circles $x^2 + y^2 = 144$ and $x^2 + y^2 - 15x + 12y = 0$ is

The circle $S=0$ cuts the circle $x^2+y^2-4x+2y-7=0$ orthogonally. If $(2,3)$ is the centre of the circle $S=0$,then its radius is

The number of common tangents to the two circles $x^2+y^2-8x+2y=0$ and $x^2+y^2-2x-16y+25=0$ is:

If tangents are drawn from any point $P$ on the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ to the circle $x^2 + y^2 + 2gx + 2fy + c \sin^2 \alpha + (g^2 + f^2) \cos^2 \alpha = 0$,then the angle between the tangents is:

If $(h, k)$ is the centre of the circle which passes through the origin and cuts the circles $x^2+y^2+4x+6y+12=0$ and $x^2+y^2+4x-6y+9=0$ orthogonally,then $k-2h=$

If $x^2+y^2-a^2+\lambda(x \cos \alpha+y \sin \alpha-p)=0$ is the smallest circle through the points of intersection of $x^2+y^2=a^2$ and $x \cos \alpha+y \sin \alpha=p$,where $0 < p < a$,then $\lambda=$