Circles $x^2 + y^2 + 4x + d = 0, x^2 + y^2 + 4fy + d = 0$ touch each other, if
$f\,\, = \,\, \pm \,\,2\,\sqrt {4\,\, + \;\,d} $
$f\,\, = \,\, \pm \,\,\frac{2}{{\sqrt {4\,\, - \,\,d} }}$
$f\,\, = \,\, \pm \,\,\sqrt {\frac{d}{{\left( {4\,\, + \;\,d} \right)}}} $
$f\,\, = \,\, \pm \,\,\sqrt {\frac{d}{{\left( {4\,\, - \,\,d} \right)}}} $
If the line $3x - 4y = \lambda $ touches the circle ${x^2} + {y^2} - 4x - 8y - 5 = 0$, then $\lambda $ is equal to
The equation of the normal to the circle ${x^2} + {y^2} - 2x = 0$ parallel to the line $x + 2y = 3$ is
If line $ax + by = 0$ touches ${x^2} + {y^2} + 2x + 4y = 0$ and is a normal to the circle ${x^2} + {y^2} - 4x + 2y - 3 = 0$, then value of $(a,b)$ will be
The tangent at $P$, any point on the circle ${x^2} + {y^2} = 4$, meets the coordinate axes in $A$ and $B$, then
From any point on the circle ${x^2} + {y^2} = {a^2}$ tangents are drawn to the circle ${x^2} + {y^2} = {a^2}{\sin ^2}\alpha $, the angle between them is