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

The equation of the tangent to the circle $x^2 + y^2 = a^2$ which is parallel to the line $y = mx + c$ is:

If the normals of the parabola $y^2 = 4x$ drawn at the end points of its latus rectum are tangents to the circle $(x - 3)^2 + (y + 2)^2 = r^2$,then the value of $r^2$ is

The tangent and the normal lines at the point $(\sqrt{3}, 1)$ to the circle $x^2 + y^2 = 4$ and the $x$-axis form a triangle. The area of this triangle (in square units) is

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

If $3x + y + k = 0$ is a tangent to the circle $x^{2} + y^{2} = 10$,the values of $k$ are