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

The angle between the tangents drawn from the origin to the circle $(x - 7)^2 + (y + 1)^2 = 25$ is:

The straight line $x + 2y = 1$ meets the coordinate axes at $A$ and $B$. $A$ circle is drawn through $A, B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is

$A$ tangent is drawn to the circle $2x^{2} + 2y^{2} - 3x + 4y = 0$ at point $A$ and it meets the line $x + y = 3$ at $B(2, 1)$. Then,the length of $AB$ is equal to:

The equations of the two tangents from $(-5, -4)$ to the circle $x^{2}+y^{2}+4x+6y+8=0$ are

The angle between the tangents to the circle $x^2+y^2=25$ from the point $(1,7)$ is