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

Описание: If 5x+9=0 is the directrix of the hyperbola 16x^2-9y^2=144, then its corresponding focus is,
[Main 10th April 2nd Shift 2019]
(a) (-5/3,0) (b) (-5,0)
(c) (5, 0) (d) (5/3,0)
Ans: b
Sol.
The given hyperbola is
(16x^2)/144-(9y^2)/144=1⇒x^2/9-y^2/16=1
Now, eccentricity (e)=√(1+16/9)=5/3
So, directrix of the hyperbola are
x=±a/e=±9/5
It is given that the directrix of the hyperbola is x=-9/5.
∴ Required corresponding focus is (-ae,0)=(-5,0).


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