Line $y = x + a\sqrt 2 $ is a tangent to the circle ${x^2} + {y^2} = {a^2}$ at
$\left( {\frac{a}{{\sqrt 2 }},\frac{a}{{\sqrt 2 }}} \right)$
$\left( { - \frac{a}{{\sqrt 2 }}, - \frac{a}{{\sqrt 2 }}} \right)$
$\left( {\frac{a}{{\sqrt 2 }}, - \frac{a}{{\sqrt 2 }}} \right)$
$\left( { - \frac{a}{{\sqrt 2 }},\frac{a}{{\sqrt 2 }}} \right)$
Points $P (-3,2), Q (9,10)$ and $R (\alpha, 4)$ lie on a circle $C$ with $P R$ as its diameter. The tangents to $C$ at the points $Q$ and $R$ intersect at the point $S$. If $S$ lies on the line $2 x - ky =1$, then $k$ is equal to $.........$.
The condition that the line $x\cos \alpha + y\sin \alpha = p$ may touch the circle ${x^2} + {y^2} = {a^2}$ is
If the point $(1, 4)$ lies inside the circle $x^2 + y^2-6x - 10y + p = 0$ and the circle does not touch or intersect the coordinate axes, then the set of all possible values of $p$ is the interval
The angle of intersection of the circles ${x^2} + {y^2} - x + y - 8 = 0$ and ${x^2} + {y^2} + 2x + 2y - 11 = 0,$ is
The angle between the tangents from $(\alpha ,\beta )$to the circle ${x^2} + {y^2} = {a^2}$, is