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 $i = \sqrt{-1}$)

The number of circles that touch the coordinate axes and the line with slope $-1$ and $y$-intercept $1$ is:

$A$ line $l$ meets the circle $x^2+y^2=61$ at points $A$ and $B$. Given that $P(-5, 6)$ is a point such that $PA=PB=10$,find the equation of line $l$.

Let a circle $C$ of radius $1$ and closer to the origin be such that the lines passing through the point $(3,2)$ and parallel to the coordinate axes touch it. Then the shortest distance of the circle $C$ from the point $(5,5)$ is:

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

The length of the chord intercepted by the circle $x^2+y^2-4x+4y+3=0$ on the line $x=3y+13$ is units.