The line $x\cos \alpha + y\sin \alpha = p$will be a tangent to the circle ${x^2} + {y^2} - 2ax\cos \alpha - 2ay\sin \alpha = 0$, if $p = $

The line $3x - 2y = k$ meets the circle ${x^2} + {y^2} = 4{r^2}$ at only one point, if ${k^2}$=

The lines $y - y_1 = m (x - x_1) \pm a \,\sqrt {1\,\, + \,\,{m^2}} $ are tangents to the same circle . The radius of the circle is :

The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-

Tangents drawn from the point $P(1,8)$ to the circle $x^2+y^2-6 x-4 y-11=0$ touch the circle at the points $A$ and $B$. The equation of the circumcircle of the triangle $P A B$ is

The equation of the tangent at the point $\left( {\frac{{a{b^2}}}{{{a^2} + {b^2}}},\frac{{{a^2}b}}{{{a^2} + {b^2}}}} \right)$ of the circle ${x^2} + {y^2} = \frac{{{a^2}{b^2}}}{{{a^2} + {b^2}}} $ is