QJEEM19Mab18b: JEE Main 2019 Mathematics - Class 11 JEEM19Mab18b Solution: If 5x + 9 = 0 is the directrix of the hyperbola 16x 2 – 9y 2 =…

Question

Verified Solution • 2025–26 Session moderate

If 5x + 9 = 0 is the directrix of the hyperbola 16x² – 9y² = 144, then its corresponding focus is :

Accepted Answer

{{{x^2}} \over 9} - {{{y^2}} \over {16}} = 1

\therefore

a = 3 and b = 4

{e^2} = 1 + {{{b^2}} \over {{a^2}}}

\Rightarrow {e^2} = 1 + {{16} \over 9}

\Rightarrow

e =

5 \over 3

\therefore

focus is (–ae, 0) = (–5, 0)

Step-by-Step Verified Solution