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For the standard rectangular hyperbola shown in the figure, $xy=c^2$, which statement is correct? 
AIts asymptotes are $y=x$ and $y=-x$
BIts auxiliary circle is $x^2+y^2=2c^2$
CIts asymptotes are the coordinate axes
DIts vertices are $(\pm c,0)$
Answer & Solution
Correct answer: C. Its asymptotes are the coordinate axes
The standard rectangular hyperbola is $xy=c^2$. Its asymptotes are $x=0$ and $y=0$, i.e. the coordinate axes. The lines $y=x$ and $y=-x$ are the transverse and conjugate axis directions in the rotated view, not the asymptotes. Also, the vertex shown is at $(c,c)$, not $(\pm c,0)$.
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