Question

What will be the coordinates of the foci of a rectangular hyperbola represented by the equation $x^2-y^2=8?$

• A. $(-4,0)$
• B. $(4,0)$
• C. $(-2,0)$
• D. $(2,0)$

Answer 1

Answer: (A), (B)

$(4,0)$

Given: Rectangular hyperbola $x^2-y^2=8$

To Find: Coordinates of foci

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

Comparing it with the given equation, $a^2=8$

$\Rightarrow a=2\sqrt{2}$

The coordinates of foci of a rectangular hyperbola is given by $(\pm a\sqrt{2},0)$.

Substituting the value of $a$ in the foci coordinates.

$(\pm (2\sqrt{2})\times (\sqrt{2}),0)$

$\Rightarrow (\pm 4,0)$