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10-2. Parabola, Ellipse, Hyperbola
hard
બિંદુ $ (1, 2)$ માંથી ઉપવલય $ 3x^2 + 2y^2 = 5$ પર દોરાતા સ્પર્શકોની જોડ વચ્ચેનો ખૂણો.....
A
${\tan ^{ - 1}}\left( {\frac{{12}}{5}} \right)$
B
${\tan ^{ - 1}}\left( {6\sqrt 5 } \right)$
C
${\tan ^{ - 1}}\left( {\frac{{12}}{{\sqrt 5 }}} \right)$
D
${\tan ^{ - 1}}\left( {12\sqrt 5 } \right)$
Solution
${\rm{S}}{{\rm{S}}_{\rm{1}}}\,\, = \,\,{T^2}$
$\tan \,\,\theta \,\, = \,\,2\,\,\frac{{\sqrt {{h^2}\,\, – \,\,ab} }}{{a\,\, + \;\,b}},\,\,$
કે જ્યાં $a\,\, = \,\,9,\,\,b\,\, = \,\, – 4\,$ અને $\,h\,\, = \,\, – 12$
$\tan \,\,\theta \,\, = \,\,2\,\,\frac{{\sqrt {{(-12)^2}\,\, – \,\,(-36)} }}{{5}},\,\,$
$\theta \,\, = {\tan ^{ – 1}}\left( {\frac{{12}}{{\sqrt 5 }}} \right)$
Standard 11
Mathematics
