If $\theta $ is the angle subtended at $P({x_1},{y_1})$ by the circle $S \equiv {x^2} + {y^2} + 2gx + 2fy + c = 0$, then
$\cot \theta = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$
$\cot \frac{\theta }{2} = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$
$\tan \theta = \frac{{2\sqrt {{g^2} + {f^2} - c} }}{{\sqrt {{s_1}} }}$
None of these
$S_1$ and $S_2$ are two concentric circles of radii $1$ and $2$ respectively. Two parallel tangents to $S_1$ cut off an arc from $S_2$. The length of the arc is
If the tangents drawn at the point $O (0,0)$ and $P (1+\sqrt{5}, 2)$ on the circle $x ^{2}+ y ^{2}-2 x -4 y =0$ intersect at the point $Q$, then the area of the triangle $OPQ$ is equal to
If the line $x = k$ touches the circle ${x^2} + {y^2} = 9$, then the value of $k$ is
Let the tangents at two points $A$ and $B$ on the circle $x ^{2}+ y ^{2}-4 x +3=0$ meet at origin $O (0,0)$. Then the area of the triangle of $OAB$ is.
The equation of the circle having the lines $y^2 - 2y + 4x - 2xy = 0$ as its normals $\&$ passing through the point $(2 , 1)$ is :