$A$ circle is such that $(x-2) \cos \theta + (y-2) \sin \theta = 1$ touches it for all values of $\theta$. Then,the circle is

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

Two common tangents to the circle ${x^2} + {y^2} = 2{a^2}$ and the parabola ${y^2} = 8ax$ are

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?

Two sides of a square are along the lines $x=-5$ and $y=4$. The point of intersection of the diagonals is $(3,-4)$. The point of intersection of the tangents drawn to the circumcircle of the square at the two consecutive vertices lying on $x=-5$ is

If the circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$ cuts each of the three circles $x^2 + y^2 + 4x + 4y + 7 = 0$,$x^2 + y^2 - 4x + 4y + 7 = 0$,and $x^2 + y^2 - 4x - 4y + 7 = 0$ orthogonally,then the equation of the tangent drawn at the point $(\sqrt{3}, 2)$ to the circle $S = 0$ is