Question

What are the parametric coordinates of a point on conjugate rectangular hyperbola whose equation is
$x^2-y^2=-6$

• A. $(\sqrt{6}\tan \theta ,\sqrt{6}\sec \theta )$
• B. $(-\sqrt{6}\tan \theta ,-\sqrt{6}\sec \theta )$
• C. $(-\sqrt{6}\sec \theta ,-\sqrt{6}\tan \theta )$
• D. $(\sqrt{6}\sec \theta ,\sqrt{6}\tan \theta )$

Answer 1

The correct option is A $(\sqrt{6}\tan \theta ,\sqrt{6}\sec \theta )$

Given: $x^2-y^2=-6$

To Find: Parametric coordinates of a point on the conjugate rectangular hyperbola

The parametric coordinates of a point on the conjugate rectangular hyperbola are given by $(a\tan \theta ,a\sec \theta )$.

From the given hyperbola equation, we have $a=\sqrt{6}$

Hence, the parametric coordinates of a point on the conjugate rectangular hyperbola are given by $(\sqrt{6}\tan \theta ,\sqrt{6}\sec \theta )$.