If the straight line $4x + 3y + \lambda = 0$ touches the circle $2({x^2} + {y^2}) = 5$, then $\lambda $ is
$\frac{{5\sqrt 5 }}{2}$
$5\sqrt 2 $
$\frac{{5\sqrt 5 }}{4}$
$\frac{{5\sqrt {10} }}{2}$
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 straight line $y = mx + c$ touches the circle ${x^2} + {y^2} - 2x - 4y + 3 = 0$ at the point $(2, 3)$, then $c =$
Consider circle $S$ : $x^2 + y^2 = 1$ and $P(0, -1)$ on it. $A$ ray of light gets reflected from tangent to $S$ at $P$ from the point with abscissa $-3$ and becomes tangent to the circle $S.$ Equation of reflected ray is
Tangents are drawn from any point on the circle $x^2 + y^2 = R^2$ to the circle $x^2 + y^2 = r^2$. If the line joining the points of intersection of these tangents with the first circle also touch the second, then $R$ equals
If the line $lx + my + n = 0$ be a tangent to the circle ${(x - h)^2} + {(y - k)^2} = {a^2},$ then