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Find the coordinate of the foci, vertice...

Find the coordinate of the foci, vertice eccentricity and the length of the latus rectum of the hyperbola
`(y ^(2))/(9) - (x ^(2))/(27) =1 `

Text Solution

Verified by Experts

`(y^(2))/(9)-(x^(2))/(27)=1`
which is the equation of conjugate hyperbola Here, `b^(2)=9anda^(2)=27`
`rArr" "b=3anda=3sqrt(3)`
Coordinates of vertices `-=(0,pmb)-=(0,pm3)`
Eccentricity `e=sqrt(1+(a^(2))/(b^(2)))=sqrt(1+(27)/(9))=2`
Coordinates of foci `-=(0,pmbe)`
`-=(0,pm3xx2)`
`-=(0,pm6)`
Length of latus rectum `=(2a^(2))/(b)=(2xx27)/(3)=18`
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