Which of the following lines is a tangent to the circle $x^2 + y^2 = 25$ for all values of $m$?

The gradient of the tangent line at the point $(a \cos \alpha, a \sin \alpha)$ to the circle $x^2 + y^2 = a^2$ is

The tangent to the circle $x^2 + y^2 = 10$ at the point $(3, 1)$ touches the circle $x^2 + y^2 - 2\sqrt{10}x - 20y + k = 0$. Find the value of $k$.

If the line $x = k$ touches the circle $x^2 + y^2 = 9$,then the value of $k$ 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

The equation of the normal to the circle $x^2 + y^2 - 2x = 0$ parallel to the line $x + 2y = 3$ is