A hyperbola, centred at the origin, has ...

A hyperbola, centred at the origin, has transverse axis 2a. If it passes through a given point `( x_(1), y _(1)),` then its eccentricity is

A

`sqrt((x _(1)^(2) -y _(1)^(2) -a^(2))/(x _(1)^(2) - y_(1)^(2)))`

B

`sqrt((a ^(2) - x _(1)^(2)-y _(1)^(2))/(a ^(2) - x _(1)^(2)))`

C

`sqrt((a ^(2) + x_(1)^(2) + y_(1)^(2))/(a ^(2) - x _(1)^(2)))`

D

none of these

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The correct Answer is:

B

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Answer the following:A hyperbola has transverse axis of length 2sqrt2 . If it passes through (2,-3), find its equation in standard form.