The line $y = mx + c$ will be a normal to the circle with radius $r$ and centre at $(a, b)$, if
$a = mb + c$
$b = ma + c$
$r = ma - b + c$
$r = ma - b$
The line $lx + my + n = 0$ will be a tangent to the circle ${x^2} + {y^2} = {a^2}$ if
The line $y = x + c$will intersect the circle ${x^2} + {y^2} = 1$ in two coincident points, if
The equation of the normal at the point $(4,-1)$ of the circle $x^2+y^2-40 x+10 y=153$ is
Tangents drawn from origin to the circle ${x^2} + {y^2} - 2ax - 2by + {b^2} = 0$ are perpendicular to each other, if
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