The number of circles passing through the origin and touching the lines $x + y = 1$ and $x - y = 1$ is $\ldots$

The area of the region (in sq. unit) bounded by x-axis, the tangent and normal to the circle $x^2 + y^2 = 4$, drawn at a point $(1, \sqrt{3})$ is

The tangent to the circle $x^2 + y^2 = 10$ at the point $(3,1)$ touches the circle $x^2 + y^2 - 2\sqrt{10}\,x - 20y + k = 0$, then the value of $k$ is...

If the circles $x^2 + y^2 = 16$ and $x^2 + y^2 + 2ax + 4y + 4 = 0$ touch each other internally then $a =$