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) \[{{\tan }^{-1}}\left( 12\sqrt{5} \right)\]
Correct Answer: C
Solution :
The equation of the pair of tangents is given by \[S{{S}_{1}}={{T}^{2}}\]\[(3{{x}^{2}}+2{{y}^{2}}-5)({{3.1}^{2}}+{{2.2}^{2}}-5)={{(3x.1+2y.2-5)}^{2}}\] \[9{{x}^{2}}-4{{y}^{2}}-24xy+40y+30x-55=0\] further angle, \[\theta \] between them can be found by using \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{a+b}=\frac{2\sqrt{{{(12)}^{2}}-(9)(-4)}}{9+(-4)}\]\[=\frac{2\sqrt{180}}{5}=\frac{12\sqrt{5}}{5},\therefore \theta ={{\tan }^{-1}}\frac{12}{\sqrt{5}}\]
You need to login to perform this action.
You will be redirected in
3 sec
