Area Of The Quadrilateral Formed With The Foci Of The Hyperbola (X2/A2) - (Y2/B2) = 1 And (X2/A2) - (Y2/B2) = -1 Is

The foci are \( (\pm ae, 0 ) and (0 \pm ae) \)

The area = \( (1/2) d_{1}d_{2}\)

= \( (1/2)(2ae)(2ae) = 2a^{2}e^{2}\)

As we know, \( b^{2} = a^{2} (e^{2} – 1)\) \( b^{2} = a^{2}e^{2} – a^{2}\) \( \Rightarrow b^{2} + a^{2} = a^{2}e^{2}\)

Therefore, area = \( 2(a^{2} + b^{2})\)

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