Question

The distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ is

• A. 16$\sqrt{2}$
• B. $\sqrt{2}$
• C. 8$\sqrt{2}$
• D. 4$\sqrt{2}$

Answer 1

Answer: (B)

$\sqrt{2}$

Answer 2

Equation of hyperbola is

X = 8 sec θ, y = 8 tan θ ⇒ $\frac{x}{8}$ = sec θ, $\frac{y}{8}$ = tan θ

$\because$ sec² θ - tan² θ = 1 ⇒ $\frac{x^{2}}{8^{2}} - \frac{y^{2}}{8^{2}}$ = 1

Here, a = 8, b = 8

Now, e = $\sqrt{1 + \frac{b^{2}}{a^{2}}} = \sqrt{1 + \frac{8^{2}}{8^{2}}} = \sqrt{1 + 1} \Rightarrow e = \sqrt{2}$.