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 information provides the vertices and foci of the hyperbola, which allows us to determine the center, the distance between the vertices and the distance between the foci. From the distance between the vertices and the distance between the foci, we can determine the value of "a" and "c". Using these values and the center of the hyperbola, we can determine the set of parametric equations. 
Based on these calculations, the correct choice is B.

Using Following Result Find a Set of Parametric Equation of Conic