If the lengths of the chords intercepted by the circle ${x^2} + {y^2} + 2gx + 2fy = 0$ from the co-ordinate axes be $10$ and $24$ respectively, then the radius of the circle is..
$17$
$9$
$14$
$13$
The two tangents to a circle from an external point are always
A circle with centre $(a, b)$ passes through the origin. The equation of the tangent to the circle at the origin is
If the straight line $y = mx + c$ touches the circle ${x^2} + {y^2} - 2x - 4y + 3 = 0$ at the point $(2, 3)$, then $c =$
The two circles which passes through $(0,a)$ and $(0, - a)$ and touch the line $y = mx + c$ will intersect each other at right angle, if
The equations of tangents to the circle ${x^2} + {y^2} - 22x - 4y + 25 = 0$ which are perpendicular to the line $5x + 12y + 8 = 0$ are