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Question

The equation of transverse and conjugate axis of hyperbola are x+2y3=0,2xy+4=0 respectively, and their respective lengths are 2 and 23. The equation of hyberbola is

A

25(x+2y3)235(2xy+4)2=1

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B
25(2xy+4)235(x+2y3)2=1
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C
2(2xy+4)23(x+2y3)2=1
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D
2(x+2y3)23(2xy+4)2=1
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Solution

The correct option is B 25(2xy+4)235(x+2y3)2=1
Equation of hyperbola described on two perpendicular lines is :
(PN)2a2(PM2)b2=1
Where PN is perpendicular distance from point on hyperbola to conjugate axis.
And PM is perpendicular distance from point on hyperbola to transverse axis.
PN=2xy+45 and PM=x+2y35
Required equation of hyperbola is :
(2xy+45)2(12)2(x+2y35)2(13)2=1
25(2xy+4)235(x+2y3)2=1

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