A) \[8\sqrt{3}/205\]
B) \[8\sqrt{3}/209\]
C) \[8\sqrt{3}/215\]
D) None of these
Correct Answer: B
Solution :
[b] The joint equation of OA and OB is \[{{x}^{2}}-4x(y-3x)-4y(y-3x)+20{{(y-3x)}^{2}}=0\] Making the equation of the parabola homogeneous using straight line. We get \[{{x}^{2}}(1+12+180)-{{y}^{2}}(4-20)-xy(4-12+120)=0\]or \[193{{x}^{2}}+16{{y}^{2}}-112xy=0\] \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{a+b}\] \[=\frac{2\sqrt{{{56}^{2}}-193\times 16}}{193+16}=\frac{8\sqrt{3}}{209}\]
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