A) \[\sqrt{3}\]
B) \[8\sqrt{3}\]
C) \[4\sqrt{3}\]
D) \[3\sqrt{3}\]
E) \[2\sqrt{3}\]
Correct Answer: B
Solution :
Let\[OA=l,\]given,\[{{y}^{2}}=4x\] ...(i) In \[\Delta OAM\] \[\sin 30{}^\circ =\frac{AM}{l}=\frac{1}{2}\] \[\Rightarrow \] \[AM=\frac{l}{2}\] and\[\cos 30{}^\circ =\frac{OM}{l}=\frac{\sqrt{3}}{2}\Rightarrow OM=\frac{l\sqrt{3}}{2}\] The coordinate of \[A=(OM,AM)=\left( \frac{l\sqrt{3}}{2},\frac{l}{2} \right)\] which satisfy the equation of parabola Eq. (i), \[{{\left( \frac{l}{2} \right)}^{2}}=4\left( \frac{l}{2} \right)\sqrt{3}\] \[\Rightarrow \] \[\frac{{{l}^{2}}}{4}=\frac{4l\sqrt{3}}{2}\] \[\Rightarrow \] \[l=8\sqrt{3}=OA\] Which is the required length of equilateral triangle.You need to login to perform this action.
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