# 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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