Question

If the vertices and foci of a hyperbola are respectively $(\pm3,0)$ and $(\pm4,0)$ then the parametric equations of that hyperbola are

• A. $x = 3\sec\theta, y = 7\tan\theta$
• B. $x = \sqrt{3}\sec\theta, y = \sqrt{7}\tan\theta$
• C. $x = \sqrt{3}\sec\theta, y = 7\tan\theta$
• D. $x = 3\sec\theta, y = \sqrt{7}\tan\theta$

Hint:

Use $c^2 = a^2 + b^2$ to compute $b$, then apply standard parametric equations of hyperbola.

Answer 1

The Correct Option is D

Vertices at $x = \pm 3$ ⇒ $a = 3$, foci at $x = \pm 4$ ⇒ $c = 4$
$c^2 = a^2 + b^2 \Rightarrow b^2 = c^2 - a^2 = 16 - 9 = 7$
So parametric form is $x = 3\sec\theta$, $y = \sqrt{7}\tan\theta$