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If L is the length of the latus rectum o...

If `L` is the length of the latus rectum of the hyperbola for which `x=3a n dy=2` are the equations of asymptotes and which passes through the point (4, 6), then the value of `L/(sqrt(2))` is_____

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The correct Answer is:
4
The equation of hyerbola is
`(x-3)(y-2)=c^(2)`
`"or "xy-2x-3y+6=c^(2)`
It passes through (4,6). Then,
`4xx6-2xx4-3xx6+6=c^(2)`
`"or "c=2`
`therefore" Latus rectum"=2sqrt2c=2sqrt2xx2=4sqrt2`
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