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Question

For the hyperbola xy=āˆ’16. Which of the following is/are true ?

A
Length of latus rectum is 82 unit
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B
coordinates of vertices will be (4,4) and (4,4)
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C
equation of directrices will be x+y=±42
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D
Length of transverse axis is 82 unit
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Solution

The correct option is D Length of transverse axis is 82 unit
xy=16
c=4
coordinates of vertices will be points of intersection of transverse axis x+y=0 and xy=16 i.e.,
(4,4) and (4,4)
Length of transverse axis is
22c=82 unit
Now, equation of directrices will be xy=±c2=±42
Length of latus rectum =Length of thransverse axis
=22c=82 unit

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