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:

If the line $3x - 4y - k = 0 (k > 0)$ touches the circle $x^2 + y^2 - 4x - 8y - 5 = 0$ at $(a, b)$,then $k + a + b$ is equal to:

The equation of the tangent to the circle $x^2 + y^2 - 2x - 4y - 4 = 0$ which is perpendicular to $3x - 4y - 1 = 0$ is:

Consider the circle $S: x^2 + y^2 = 1$ and point $P(0, -1)$ on it. $A$ ray of light passes through the point $(-3, -1)$ and reflects from the tangent to $S$ at $P$. After reflection,it becomes tangent to the circle $S$. Find the equation of the reflected ray.

If the tangent drawn at the point $P$ on the circle $x^2+y^2+6x+6y=2$ meets the straight line $5x-2y+6=0$ at a point $Q$ on the $Y$-axis,then the length of $PQ$ 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