Using following result find a set of parametric equation of conic.
Hyperbola: $x = h + a \sec \theta , y = k + b \tan \theta$
Hyperbola: vertices: $( \pm 15,0 )$ ;foci: $( \pm 17,0 )$
A) $x = 8 \sec \theta , y = 15 \tan \theta$
B) $x = 17 - 15 \sec \theta , y = 17 + 8 \tan \theta$
C) $x = 15 \sec \theta , y = 8 \tan \theta$
D) $x = - 8 + 15 \sec \theta , y = 17 - 8 \tan \theta$
E) $x = 17 \sec \theta , y = 17 \tan \theta$

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: $( \pm 15,0 )$ ;foci: $( \pm 17,0 )$ ​
A) $x = 8 \sec \theta , y = 15 \tan \theta$
B) $x = 17 - 15 \sec \theta , y = 17 + 8 \tan \theta$
C) $x = 15 \sec \theta , y = 8 \tan \theta$
D) $x = - 8 + 15 \sec \theta , y = 17 - 8 \tan \theta$
E) $x = 17 \sec \theta , y = 17 \tan \theta$

Quizplus · Accepted Answer

The given information of vertices and foci suggests that the hyperbola is a horizontal one. 
Let the center of the hyperbola be (h,k), then the coordinates of the vertices are (h±a,k) and the coordinates of the foci are (h±c,k), where a is the distance between the center and the vertices and c is the distance between the center and the foci. 
From the given information, we can conclude that h=11ea99db_b7f3_94ac_c9e3ec9ffea5_TB4590_11 and k=11ea99db_b7f3_b0f0_94ac_053d57991908_TB4590_11 (since the center is midway between the vertices and foci along the x-axis). 
Also, we can calculate a and c using the distance formula: a=sqrt(99)=3*sqrt(11) and c=sqrt(100)=10. 
Therefore, the set of parametric equations would be: 
x=h+a*sec(t) and y=k+b*tan(t), where b=sqrt(c^2-a^2)=sqrt(71). 
Substituting the values, we get x=11ea99db_b7f3_d804_94ac_ab58a7a39075_TB4590_11+3sqrt(11)*sec(t) and y=11ea99db_b7f3_b0f0_94ac_053d57991908_TB4590_11+sqrt(71)*tan(t). 
Hence, the best choice is C.

Using Following Result Find a Set of Parametric Equation of Conic