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

Step-by-step solution

The equation of a hyperbola in standard form is x 2 a 2 - y 2 b 2 = 1 and its foci are ± a e ,   0 and directrices are x = ± a e . The given equation of hyperbola is 16 x 2 - 9 y 2 = 144 ,     ⇒ x 2 9 - y 2 16 = 1 ⇒ a 2 = 9 ,   b 2 = 16 Given, directrix of the hyperbola is 5 x + 9 = 0 ,     ⇒ x = - 9 5 . Hence, on comparing the directrix with the standard equation, we get a e = 9 5 ⇒ 3 e = 9 5 ⇒ e = 5 3 And, hence the required focus is - a e , &#