The number of common tangents to the circles $x^2+y^2-x=0$ and $x^2+y^2+x=0$ is/are:

If the lines $12x - 5y - 17 = 0$ and $24x - 10y + 44 = 0$ are tangents to the same circle,then the radius of the circle is:

Let $P$ and $Q$ be any points on the curves $(x-1)^{2}+(y+1)^{2}=1$ and $y=x^{2}$,respectively. The distance between $P$ and $Q$ is minimum for some value of the abscissa of $P$ in the interval

Find the equation of the circumcircle of the triangle formed by the lines $y \pm \sqrt{3}x = 6$ and the $x$-axis.

If $z_1$ is a point on $z\bar{z} = 1$ and $z_2$ is another point on $(4 - 3i)z + (4 + 3i)\bar{z} - 15 = 0$,then $|z_1 - z_2|_{min}$ is (where $i = \sqrt{-1}$)

Let $R$ be the region of the disc $x^2+y^2 \leq 1$ in the first quadrant. Then,the area of the largest possible circle contained in $R$ is