The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is $\pi /4$ is :
The area of the rectangle formed by the perpendiculars from the centre of the standard ellipse to the tangent and normal at its point whose eccentric angle is $\pi /4$ is :
- A
$\frac{{\left( {{a^2}\,\, - \,\,{b^2}} \right)\,\,ab}}{{{a^2}\,\, + \,\,{b^2}}}$
- B
$\frac{{\left( {{a^2} - {b^2}} \right)}}{{\left( {{a^2} + {b^2}} \right)ab}}$
- C
$\frac{{\left( {{a^2}\,\, - \,\,{b^2}} \right)}}{{ab\,\,\left( {{a^2}\,\, + \,\,{b^2}} \right)}}$
- D
$\frac{{{a^2}\,\, + \,\,{b^2}}}{{\left( {{a^2}\,\, - \,\,{b^2}} \right)\,\,ab}}$
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