A) \[{{\tan }^{-1}}\frac{3}{2}\]
B) \[{{\tan }^{-1}}\frac{4}{5}\]
C) \[{{90}^{o}}\]
D) None of these
Correct Answer: C
Solution :
The equation of any curve through the points of intersection of the given curves is \[2{{x}^{2}}+3{{y}^{2}}+10x+\lambda (3{{x}^{2}}+5{{y}^{2}}+16x)=0\] .....(i) If this equation represents two straight lines through the origin, then this must be homogeneous equation of second degree i.e., coefficient of x in (i) must vanish \ \[10+16\lambda =0\Rightarrow \lambda =\frac{-10}{16}=\frac{-5}{8}\] Substituting this value of \[\lambda \]in (i), we get the equation of pair of straight lines \[{{x}^{2}}-{{y}^{2}}=0\] ?..(ii) Hence the lines represented by the equation (ii) are mutually perpendicular.
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