Line $y = x + a\sqrt 2 $ is a tangent to the circle ${x^2} + {y^2} = {a^2}$ at
$\left( {\frac{a}{{\sqrt 2 }},\frac{a}{{\sqrt 2 }}} \right)$
$\left( { - \frac{a}{{\sqrt 2 }}, - \frac{a}{{\sqrt 2 }}} \right)$
$\left( {\frac{a}{{\sqrt 2 }}, - \frac{a}{{\sqrt 2 }}} \right)$
$\left( { - \frac{a}{{\sqrt 2 }},\frac{a}{{\sqrt 2 }}} \right)$
If the line $y = \sqrt 3 x + k$ touches the circle ${x^2} + {y^2} = 16$, then $k =$
The point at which the normal to the circle ${x^2} + {y^2} + 4x + 6y - 39 = 0$ at the point $(2, 3)$ will meet the circle again, is
From the origin chords are drawn to the circle ${(x - 1)^2} + {y^2} = 1$. The equation of the locus of the middle points of these chords is
If the line $y$ $\cos \alpha = x\sin \alpha + a\cos \alpha $ be a tangent to the circle ${x^2} + {y^2} = {a^2}$, then
The tangent at $P$, any point on the circle ${x^2} + {y^2} = 4$, meets the coordinate axes in $A$ and $B$, then