At which point does the line $3x + 4y = 25$ touch the circle $x^2 + y^2 = 25$?

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 slope of the normal to the circle $x^2+y^2+2gx+2fy+c=0$ at $(x_1, y_1)$ is

If the tangents drawn at the points $O(0,0)$ and $P(1+\sqrt{5}, 2)$ on the circle $x^{2}+y^{2}-2x-4y=0$ intersect at the point $Q$,then the area of the triangle $OPQ$ is equal to

The condition that the line $x \cos \alpha + y \sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is

For what possible value of $p$ is the line $x \cos \alpha + y \sin \alpha = p$ a tangent to the circle $x^2 + y^2 - 2qx \cos \alpha - 2qy \sin \alpha = 0$?