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
The line $x\cos \alpha + y\sin \alpha = p$will be a tangent to the circle ${x^2} + {y^2} - 2ax\cos \alpha - 2ay\sin \alpha = 0$, if $p = $
If $a > 2b > 0$ then the positive value of m for which $y = mx - b\sqrt {1 + {m^2}} $ is a common tangent to ${x^2} + {y^2} = {b^2}$ and ${(x - a)^2} + {y^2} = {b^2}$, is
The equations of the normals to the circle ${x^2} + {y^2} - 8x - 2y + 12 = 0$ at the points whose ordinate is $-1,$ will be
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Let $A B$ be a chord of length $12$ of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$ If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$, then five times the distance of point $P$ from chord $AB$ is equal to$.......$