If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is
$2$ but not $-2$
$-2$ but not $2$
$3$
None of these
If the straight line $ax + by = 2;a,b \ne 0$ touches the circle ${x^2} + {y^2} - 2x = 3$ and is normal to the circle ${x^2} + {y^2} - 4y = 6$, then the values of a and b are respectively
The area of the triangle formed by the positive $x$-axis and the normal and the tangent to the circle $x^2 + y^2 = 4$ at $(1, \sqrt 3 )$ is
The equations of the tangents to the circle ${x^2} + {y^2} = 13$ at the points whose abscissa is $2$, are
The line $x = y$ touches a circle at the point $(1, 1)$. If the circle also passes through the point $(1, -3)$, then its radius is
The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if