The line $y = x + c$will intersect the circle ${x^2} + {y^2} = 1$ in two coincident points, if
$c = \sqrt 2 $
$c = - \sqrt 2 $
$c = \pm \sqrt 2 $
None of these
Length of the tangent drawn from any point on the circle ${x^2} + {y^2} + 2gx + 2fy + {c_1} = 0$ to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ is
Two tangents drawn from the origin to the circle ${x^2} + {y^2} + 2gx + 2fy + c = 0$ will be perpendicular to each other, if
The equations of the tangents to the circle ${x^2} + {y^2} = 13$ at the points whose abscissa is $2$, are
The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-
The equation of circle which touches the axes of coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is ${x^2} + {y^2} - 2cx - 2cy + {c^2} = 0$, where $c$ is