If `S_1a n dS_2` are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and `S_3a n dS_4` are the foci of the conjugate hyperbola, then the area of quadrilateral `S_1S_3S_2S_4` is 24 (b) 26 (c) 22 (d) none of these

Options

A. 24
B. 26
C. 22
D. none of these

Answer

B

Explanation

`"Required area"=4xx"Area of "DeltaS_(2)OS_(4)=4xx(1)/(2)asxxbe_(1)`
`=4xx(1)/(2)xx2xx3xxee_(1)`
`b^(2)=a^(2)(e^(2)-1)`
`"or "e^(2)=(9)/(4)+1=(13)/(4)`
Also, `(1)/(e_(1)^(2))=1-(1)/(e^(2))=1-(4)/(13)=(9)/(13)`
`"or "e_(1)^(2)=(13)/(9)`
`"Required area"=12xx(sqrt(13))/(2)xx(sqrt(13))/(3)`
`=2xx13=26`