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
A line $lx + my + n = 0$ meets the circle ${x^2} + {y^2} = {a^2}$ at the points $P$ and $Q$. The tangents drawn at the points $P$ and $Q$ meet at $R$, then the coordinates of $R$ is
The gradient of the normal at the point $(-2, -3)$ on the circle ${x^2} + {y^2} + 2x + 4y + 3 = 0$ is
The set of all values of $a^2$ for which the line $x + y =0$ bisects two distinct chords drawn from a point $P\left(\frac{1+a}{2}, \frac{1-a}{2}\right)$ on the circle $2 x ^2+2 y ^2-(1+ a ) x -(1- a ) y =0$ is equal to:
If the straight line $4x + 3y + \lambda = 0$ touches the circle $2({x^2} + {y^2}) = 5$, then $\lambda $ is
A pair of tangents are drawn to a unit circle with centre at the origin and these tangents intersect at A enclosing an angle of $60^o$. The area enclosed by these tangents and the arc of the circle is