The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if
${n^2}({l^2} + {m^2}) = {a^2}$
${a^2}({l^2} + {m^2}) = {n^2}$
$n(l + m)a$
$a(l + m) = n$
The equation of circle with centre $(1, 2)$ and tangent $x + y - 5 = 0$ is
Consider the following statements :
Assertion $(A)$ : The circle ${x^2} + {y^2} = 1$ has exactly two tangents parallel to the $x$ - axis
Reason $(R)$ : $\frac{{dy}}{{dx}} = 0$ on the circle exactly at the point $(0, \pm 1)$.
Of these statements
The angle between the pair of tangents from the point $(1, 1/2)$ to the circle $x^2 + y^2 + 4x + 2y -4=0$ is-
If the tangent to the circle ${x^2} + {y^2} = {r^2}$ at the point $(a, b)$ meets the coordinate axes at the point $A$ and $B$, and $O$ is the origin, then the area of the triangle $OAB$ is
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