Question

What will be the equation of directrices of a rectangular hyperbola represented by the equation $x^2-y^2=16?$

• A. $x=2\sqrt{2}$
• B. $x=-4\sqrt{2}$
• C. $x=4\sqrt{2}$
• D. $x=-2\sqrt{2}$

Answer 1

Answer: (A), (D)

$x=-2\sqrt{2}$

Given: Rectangular hyperbola $x^2-y^2=16$

To Find: Equation of directrices

We know that, the standard equation of a rectangular hyperbola is $x^2-y^2=a^2$.

Comparing it with the given equation, $a^2=16$

$\Rightarrow a=4$

The coordinates of foci of a rectangular hyperbola is given by $x=\pm \frac{a}{\sqrt{2}}$.

Substituting the value of $a$ in the directrix equation.

$x=\pm \frac{4}{\sqrt{2}}$

$\Rightarrow x=\pm 2\sqrt{2}$