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If \mathrm{S_1}and \mathrm{S_2} are the foci of the hyperbola whose length of the tranverse axis is 4 and that of the conjugate axis is 6 , and \mathrm{S_3} and \mathrm{S_4} are the foci of the conjugate hyperbola, then the area of quadrilateral  \mathrm{S_1 S_2 S_3 S_4 } is

Option: 1

30


Option: 2

22


Option: 3

26


Option: 4

44


Answers (1)

best_answer

 Required area =4 \times area of \mathrm{ \Delta S_2 O S_4}

\begin{aligned} &\mathrm{ =4 \times \frac{1}{2} \times 2 \times 3 \times c e_1 }\\ \mathrm{b^2} &\mathrm{ =a^2\left(e^2-1\right) }\\ \text { or e}^2 &\mathrm{ =\frac{9}{4}+1=\frac{13}{4}} \end{aligned}
Also, \mathrm{\frac{1}{e_1^2}=1-\frac{1}{e^2}=1-\frac{4}{13}=\frac{9}{13} ~or ~e_1^2=\frac{13}{9}}
Required area = \mathrm{12 \times \frac{\sqrt{13}}{2} \times \frac{\sqrt{13}}{3}=2 \times 13=26}

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