If the vertices and foci of a hyperbola are respectively ± 3 , 0 and ± 4 , 0 then the parametric equations of that hyperbola are

Step-by-step solution

Given, The vertices and foci of a hyperbola are respectively ± 3 , 0 and ± 4 , 0 So a = 3 and a e = 4 , then e = 4 3 Now we know that b 2 = a 2 e 2 - 1 ⇒ b 2 = 3 2 4 3 2 - 1 ⇒ b 2 = 16 - 9 = 7 ⇒ b = 7 So equation of hyperbola is given by x 2 9 - y 2 7 = 1 Now parametric equation of hyperbola is given by x = a secθ   &   y = b tan θ So, x = 3 sec θ   &   y = 7 tan θ