If the line $y=2x+c$ is a tangent to the circle $x^2+y^2=5$,then a value of $c$ is

The equations of the tangents drawn from the origin to the circle $x^2+y^2+2gx+2fy+g^2=0$ are

If the angle between the pair of tangents drawn to the circle $x^2+y^2-2x+4y+3=0$ from $(6,-5)$ is $\theta$,then $\tan \theta=$

The equation of a circle which has a tangent $3x + 4y = 6$ and two normals given by $(x - 1)(y - 2) = 0$ is

The normal to the circle given by $x^2+y^2-6x+8y-144=0$ at $(8,8)$ meets the circle again at the point

The angle between the tangents drawn from the point $(2, 2)$ to the circle $x^2 + y^2 + 4x + 4y + c = 0$ is $\cos^{-1}\left(\frac{7}{16}\right)$. If two such circles exist,then the sum of the values of $c$ is: