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Find the vertices, eccentricity foci, rquation of directrices and length of latus rectum of the hyperbola `9x^(2)-25y^(2)=225`.

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Equation of hyperbola.
`9x^(2)-25y^(2)=225`
`rArr" "(x^(2))/(25)-(y^(2))/(9)=1`
Here `a^(2)=25andb^(2)=9`
`rArr" "a=5andb=3`
Co-ordinates of vertices `=(pma,0)=(pm5,0)`.
Eccentricity e `=sqrt(1+(b^(2))/(a^(2)))=sqrt(1+(9)/(25))=sqrt(34)/(5)`.
Co-ordinates of foci
`=(pmae,0)=(pm5xx(sqrt(34))/(5),0)=(pmsqrt(34),0)`.
Equation of directrices `x=pm(a)/(e)`
`rArr""x=pm(5)/(sqrt(34)/(5))`
`rArr""x=pm(5)/(sqrt(34))`.
Length of latus rectum `=(2b^(2))/(a)=(2xx9)/(5)=(18)/(5)`.
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