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 $\tan \theta=$

If the length of the tangent drawn from the point $(5, 3)$ to the circle $x^2 + y^2 + 2x + ky + 17 = 0$ is $7$,then the value of $k$ is:

The diagonals of a rectangle have endpoints at $(0, 0)$ and $(8, 6)$. The equations of the tangents to the circumcircle of the rectangle,which are parallel to these diagonals,are:

Statement $(A) :$ For all values of $\theta$,the line $(x - 3) \cos \theta + (y - 3) \sin \theta = 1$ is tangent to the circle $(x - 3)^2 + (y - 3)^2 = 1$.
Reason $(R) :$ For all values of $\theta$,the line $x \cos \theta + y \sin \theta = a$ is tangent to the circle $x^2 + y^2 = a^2$.

Find the equation of the circle having normals $(x-1)(y-2)=0$ and a tangent $3x+4y=6$.

The angle between the tangents drawn from a point $(4,3)$ to the circle $x^2+y^2-2x-4y=0$ is