The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$,if

Let the tangent to the circle $x^{2}+y^{2}=25$ at the point $R(3,4)$ meet the $x$-axis and $y$-axis at points $P$ and $Q$,respectively. If $r$ is the radius of the circle passing through the origin $O$ and having its centre at the incentre of the triangle $OPQ$,then $r^{2}$ is equal to

The equation of the normal to a circle at the point $\left( 3 + \frac{3}{\sqrt{2}}, \frac{3}{\sqrt{2}} \right)$ is $y - x + 3 = 0$. To which of the following circles does this normal belong?

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

If $a > 2b > 0$,then the positive value of $m$ for which $y = mx - b\sqrt{1 + m^2}$ is a common tangent to $x^2 + y^2 = b^2$ and $(x - a)^2 + y^2 = b^2$ is:

The line $y = x + a\sqrt{2}$ is a tangent to the circle $x^2 + y^2 = a^2$ at which of the following points?