question_answer

The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\]and \[x=a\], is                      

A)            \[2{{a}^{2}}\]                       

B)            \[\frac{{{a}^{2}}}{2}\]

C)            \[\frac{\sqrt{3}{{a}^{2}}}{2}\]                                           

D)            \[\frac{2{{a}^{2}}}{\sqrt{3}}\]

Correct Answer: B

Solution :

           According to the figure,     Area = \[\frac{1}{2}\left| \text{ }\begin{matrix}    0 & 0 & 1  \\    a & -\frac{a}{2} & 1  \\    a & \frac{a}{2} & 1  \\ \end{matrix}\text{ } \right|\]\[=\frac{{{a}^{2}}}{2}\].