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Question

The equation of the directrices of the rectangular hyperbola xy=c2 :

A
x+y=c2
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B
x+y=c
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C
xy=c2
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D
xy=c
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Solution

The correct option is A x+y=c2
for rectangular hyperbola, xy=c2
b=a=c2
Therefore, the co-ordinates of foci are given by x=y=±a2+a22a
=±a=±c2
Equation of direction for hyperbola x2y2=a2 is
x=±ae=±a2
Now, rotating the axes through 45O that is writing xcos(45O)ysin(45O) for x.
x+y2=±a2x+y=±a
x+y=±c2

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