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Question

Which of the following is correct for a rectangular hyperbola
xy=18?

A
Foci: (6,6) and (6,6)
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B
Eccentricity =2
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C
Directrix: x+y=±6
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D
Focal length288
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Solution

The correct option is D Focal length288
Given, xy=18c=32

Foci: (2c,2c) and (2c,2c)

Foci:(6,6) and (6,6)

Focal length =4c Focal length =4×32 Focal length =122 Focal length =288

Directrix: x+y=±2c
x+y=±2×32
x+y=±6

For a rectangular hyperbola
Eccentricity =2

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