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)}}} $
The equation of the tangent to the circle ${x^2} + {y^2} = {a^2}$ which makes a triangle of area ${a^2}$ with the co-ordinate axes, is
If $OA$ and $OB$ be the tangents to the circle ${x^2} + {y^2} - 6x - 8y + 21 = 0$ drawn from the origin $O$, then $AB =$
The equation of the chord of the circle ${x^2} + {y^2} = {a^2}$ having $({x_1},{y_1})$ as its mid-point is
The number of tangents that can be drawn from $(0, 0)$ to the circle ${x^2} + {y^2} + 2x + 6y - 15 = 0$ is
The condition that the line $x\cos \alpha + y\sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is