If the acute angle between the pair of tangents drawn from the origin to the circle $x^2+y^2-4x-8y+4=0$ is $\alpha$,then $\tan \alpha=$

$3x + 4y - 43 = 0$ is a tangent to the circle $S \equiv x^2 + y^2 - 6x + 8y + k = 0$ at a point $P$. If $C$ is the centre of the circle and $Q$ is a point which divides $CP$ in the ratio $-1:2$,then the power of the point $Q$ with respect to the circle $S = 0$ is

The equation of a line passing through $(7, 4)$ and touching the circle $x^2 + y^2 - 6x + 4y - 3 = 0$ is:

If the line $y = mx + c$ is a tangent to the circle $x^2 + y^2 = a^2$,then the point of contact is

The equation of the line passing through the point $(x', y')$ and perpendicular to the line $yy' = 2a(x + x')$ is

The square of the length of the tangent drawn from the point $(\alpha, \beta)$ to the circle $ax^2 + ay^2 = r^2$ is