If θ is angle subtended at P({x₁},{y₁}) by circle S equiv {x^2} + {y^2} + 2gx + 2fy + c = 0 , t

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10-1.Circle and System of Circles

easy

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

A

$\cot \theta = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$

B

$\cot \frac{\theta }{2} = \frac{{\sqrt {{s_1}} }}{{\sqrt {{g^2} + {f^2} - c} }}$

C

$\tan \theta = \frac{{2\sqrt {{g^2} + {f^2} - c} }}{{\sqrt {{s_1}} }}$

D

None of these

Solution

(b) $\cot \frac{\theta }{2} = \frac{{P{T_1}}}{{C{T_1}}} $

$= \frac{{\sqrt {{S_1}} }}{{\sqrt {{g^2} + {f^2} – c} }}$

Standard 11

Mathematics

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