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

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2 \sqrt{2} c units

4 \sqrt{2} c units

3 \sqrt{2} c units

\sqrt{2} c units

answer is A.

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Detailed Solution

Given equation of rectangular hyperbola,

xy = c^{2}

Here, the transverse axis is along line

y = x

. So, put y =x in above equation,

\Rightarrow x^{2} = c^{2}

\Rightarrow x = \pm c

At,

x = c

\Rightarrow y = c

At,

x = - c

\Rightarrow y = - c

So, the points we get, (c, c) and (−c, −c).
Here the distance between these points,

d = \sqrt{(- c - c)^{2} + (- c - c)^{2}}

d = \sqrt{4 c^{2} + 4 c^{2}}

d = \sqrt{8 c^{2}}

d = 2 \sqrt{2} c units

Option 1 is correct.

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