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If 5x + 9 = 0 is the directrix of the hy...

If 5x + 9 = 0 is the directrix of the hyperbola `16x^(2)-9y^(2)=144` then its corresponding focus is

A

`(-(5)/(3),0)`

B

`(-5,0)`

C

`((5)/(3),0)`

D

`(5,0)`

Text Solution

Verified by Experts

Equation of given hyperbola is
`16x^(2)-9y^(2)=144`
`rArr (x^(2))/(9)-(y^(2))/(16)=1 " ...(i)" `
So, the eccentricity of Eq. (i)
`e=sqrt(1+(16)/(9))=(5)/(3)`
[` because ` the eccentricity (e) of the hyperbola `(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` is `sqrt(1+(b//a)^(2))`]
and given directrix is `5x+9=0 rArr x= -9//5`
So, corresponding focus is `(-3((5)/(3)),0)=(-5,0)`
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