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if 5x+9=0 is the directrix of the hyperb...

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

A

`(5,0)`

B

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

C

`(-5,0)`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`(x^(2))/(9) - (y^(2))/(16) = 1`
`b^(2) = a^(2) (e^(2) -1)`
`16 = 9 (e^(2) -1) rArr e = (5)/(3)` ....(1)
`-(a)/(e) = (-9)/(5) rArr (a)/(e) = (9)/(5)`
`(-ae, 0) = (-5, 0)`
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