If the lengths of the chords intercepted by the circle $x^2 + y^2 + 2gx + 2fy = 0$ from the coordinate axes are $10$ and $24$ respectively,then the radius of the circle is:

Let $C_1$ and $C_2$ be two circles touching each other externally at point $A$. Let $AB$ be the diameter of circle $C_1$. Draw a secant $BA_3$ to circle $C_2$,intersecting circle $C_1$ at point $A_1$ (where $A_1 \neq A$) and circle $C_2$ at points $A_2$ and $A_3$. If $BA_1 = 2$,$BA_2 = 3$,and $BA_3 = 4$,then the radii of circles $C_1$ and $C_2$ are respectively:

If $\theta$ is the angle between the circles $x^2+y^2-4x+2y-4=0$ and $x^2+y^2-2x+4y-11=0$,then $\sin \theta=$

If a circle passes through the points of intersection of the lines $\lambda x - y + 1 = 0$ and $x - 2y + 3 = 0$ with the coordinate axes,then the value of $\lambda$ is:

The length of the chord joining points $(4 \cos \theta, 4 \sin \theta)$ and $(4 \cos (\theta+60^{\circ}), 4 \sin (\theta+60^{\circ}))$ on the circle $x^2+y^2=16$ is

If $(6, -k)$ and $(-3, 2)$ are conjugate points with respect to the circle $x^2 + y^2 + 6x + 4y + 12 = 0$,then $k$ equals: