Using following result find a set of parametric equation of conic.
Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$
Hyperbola: vertices: $( \pm 4,0 )$ ; foci: $( \pm 5,0 )$
A) $x = 5 + 4 \sec \theta , y = 5 + 3 \tan \theta$
B) $x = 4 \sec \theta , y = 3 \tan \theta$
C) $x = 5 - 4 \sec \theta , y = 3 \tan \theta$
D) $x = 3 \sec \theta , y = 4 \tan \theta$
E) $x = 5 \sec \theta , y = 4 \tan \theta$

Question

Using following result find a set of parametric equation of conic. 
Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$ 
Hyperbola: vertices: $( \pm 4,0 )$ ; foci: $( \pm 5,0 )$ 
A) $x = 5 + 4 \sec \theta , y = 5 + 3 \tan \theta$
B) $x = 4 \sec \theta , y = 3 \tan \theta$
C) $x = 5 - 4 \sec \theta , y = 3 \tan \theta$
D) $x = 3 \sec \theta , y = 4 \tan \theta$
E) $x = 5 \sec \theta , y = 4 \tan \theta$

Quizplus · Accepted Answer

The given hyperbola has its center at the origin (h = 0, k = 0) because the vertices are symmetrically placed about the origin. The distance from the center to a vertex is the value of 'a', which is 4 in this case. The distance from the center to a focus (c) is 5, but this information is not directly used in the parametric equations. The value of 'b' can be found using the relationship $c^2 = a^2 + b^2$ for hyperbolas, which gives $b = \sqrt{c^2 - a^2} = \sqrt{5^2 - 4^2} = \sqrt{25 - 16} = \sqrt{9} = 3$. Therefore, the correct parametric equations, with h = 0 and k = 0, are $x = 4 \sec \theta$ and $y = 3 \tan \theta$.

Using Following Result Find a Set of Parametric Equation of Conic