Question

If $S_1$ and $S_2$ are the foci of the hyperbola whose transverse axis length is $4$ and conjugate axis length is $6$. $S_3$ and $S_4$ are the foci of the conjugate hyperbola, then the area of the quadrilateral $S_1{S}_3{S}_2{S}_4$ is :

• A. $24$
• B. $26$
• C. $22$
• D. None of these

Answer 1

The correct option is B $26$

We know that "The quadrilateral formed by the hyperbola and conjugate hyperbola is a square "
Required Area $=(S_1{S}_3{)}^2$
$(S_1{S}_3{)}^2=a^2{e_1}^2+b^2{e_2}^2$
$=a^2(1+\frac{b^2}{a^2})+b^2(1+\frac{a^2}{b^2})$
$=2(a^2+b^2)$
Area of quadrilateral $=26$ sq.units