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

Question

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)

Solutions · 1