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 $i = \sqrt{-1}$)

If the circles $x^2+y^2+2hx+2ky=0$ and $x^2+y^2+2h'x+2k'y=0$ touch each other,then $\frac{h'k}{hk'} = $

The straight line $2x - 3y = 1$ divides the circular region $x^2 + y^2 \leq 6$ into two parts. If $S = \left\{ \left(2, \frac{3}{4}\right), \left(\frac{5}{2}, \frac{3}{4}\right), \left(\frac{1}{4}, -\frac{1}{4}\right), \left(\frac{1}{8}, \frac{1}{4}\right) \right\}$,then the number of point$(s)$ in $S$ lying inside the smaller part is

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

The line $y=mx+c$ intercepts the circle $x^2+y^2=r^2$ in two distinct points,if

The number of common tangents to the circles $x^2 + y^2 - 2x + 4y - 4 = 0$ and $x^2 + y^2 - 8x - 4y + 16 = 0$ is: