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10-1.Circle and System of Circles
hard
જો વર્તૂળ $S = x^2 + y^2 + 2gx + 2fy + c = 0$ દ્વારા બિંદુ $P(x_1, y_1) $ આગળ બનતો ખૂણો $\theta$ હોય, તો....
A
$\tan \,\theta \, = \,\,\frac{{2\,\,\sqrt {{g^2}\,\, + \;\,{{{f}}^2}\,\, - \,\,c} }}{{\sqrt {{S_1}} }}$
B
$\cot \,\,\frac{\theta }{2}\,\,\frac{{\sqrt {{S_1}} }}{{\sqrt {{g^2}\,\, + \;\,{{{f}}^2}\,\, - \,\,c} }}$
C
$\cot \,\,\theta \,\, = \,\frac{{\sqrt {{S_1}} }}{{\sqrt {{g^2}\,\, + \;{{{f}}^2}\, - \,\,c} }}$
D
એકપણ નહિ
Solution
$\,cot\,\frac{\theta }{2}\, = \,\,\frac{{P{T_1}}}{{C{T_1}}}\,\, = \,\frac{{\sqrt {{S_1}} }}{{\sqrt {{g^2} + {{f}^2} – c} }}$
Standard 11
Mathematics
