Find The Coordinates Of The Foci And The Equation Of The Directrices Of The Rectangular Hyperbola xy = c2.

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Find the coordinates of the foci and the equation of the directrices of the rectangular hyperbola xy = c2.


Correct option is


Reference to transverse and conjugate axes, as coordinate axes, the equation of hyperbola is



If e be the eccentricity, then  


∴ Coordinates of foci are   

Also its direction are  


Now rotating the coordinate axes through an angle –π/4, the equation of hyperbola reduces to xy = c2 where c2 = a2/2, by putting  for x and y.    

∴ For foci, we get 





Also the equations of the directrices reduce to 





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