For rectangular hyperbola $x y = c^{2}$ , What is the length of transverse axis, length of conjugate axis and length of latus rectum

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Solution

$x y = c^{2}$
Transverse axis is along the line $y = x$
$\Rightarrow x^{2} = c^{2}$
$\Rightarrow x = \pm c$
$x = c \Rightarrow y = c$
$x = - c \Rightarrow y = - c$
Distance between the points $(c, c)$ and $(- c, - c)$
$= \sqrt{{(- c - c)}^{2} + {(- c - c)}^{2}}$
$= \sqrt{8 c^{2}} = 2 \sqrt{2} c$ units

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For rectangular hyperbola xy=c2, What is the length of transverse axis, length of conjugate axis and length of latus rectum

xy=c2Transverse axis is along the line y=x⇒x2=c2⇒x=±cx=c⇒y=cx=−c⇒y=−cDistance between the points (c,c) and (−c,−c)=√(−c−c)2+(−c−c)2=√8c2=2√2c units

For rectangular hyperbola $x y = c^{2}$ , What is the length of transverse axis, length of conjugate axis and length of latus rectum