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Find the coordinate of the foci, vertice...

Find the coordinate of the foci, vertices, eccentricity and the length of the latus rectum of the hyperbola
`9y ^(2) - 4x ^(2) = 36`

Text Solution

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Equation of hyperbola
`9y^(2)-4x^(2)=36`
`rArr(y^(2))/(4)-(x^(2))/(9)=1`
Here, the transverse axis is along y-axis.
Comparing with `(y^(2))/(b^(2))-(x^(2))/(a^(2))=1`
`b^(2)=4," "a^(2)=9`
`rArr" "b=2," "a=3`
Now, vertices `-=(0,pmb)-=(0,pm2)`
Eccentricity `e=sqrt(1+(a^(2))/(b^(2)))=sqrt(1+(9)/(4))`
`=sqrt((13)/(4))=(sqrt(13))/(2)`
Now, be `=2xx(sqrt(13))/(2)sqrt(13)`
`:.` Coordinates of foci `-=(0,pmbe)-=(0,pmsqrt(13))`
Length of latus rectum `=(2a^(2))/(b)=(2xx9)/(2)=9`
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