The circle $x^2 + y^2 - 4x - 4y + 4 = 0$ is...

Let $C$ be the centre of the circle $x^{2}+y^{2}-x+2 y=\frac{11}{4}$ and $P$ be a point on the circle. $A$ line passes through the point $C$,makes an angle of $\frac{\pi}{4}$ with the line $CP$ and intersects the circle at the points $Q$ and $R$. Then the area of the triangle $PQR$ (in unit$^{2}$) is.

The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2y$ is

If the power of the point $(1, 6)$ with respect to the circle $x^2 + y^2 + 4x - 6y - a = 0$ is $-16$,then $a$ equals:

The equation of the circle having the lines $x^2 + 2xy + 3x + 6y = 0$ as its normals and having a size just sufficient to contain the circle $x(x - 4) + y(y - 3) = 0$ is

$A$ circle $C_1$ of radius $2$ touches both $x$-axis and $y$-axis. Another circle $C_2$ whose radius is greater than $2$ touches circle $C_1$ and both the axes. Then the radius of circle $C_2$ is