Question

The family of the curves which intersects the family of rectangular hyperbola $xy=c^2$ orthogonally is

• A. family of parabola
• B. family of ellipse
• C. family of circle
• D. family of rectangular hyperbola

Answer 1

The correct option is D family of rectangular hyperbola

$xy=c^2$
$\Rightarrow x\frac{dy}{dx}+y=0$
Replacing $\frac{dy}{dx}by-\frac{dx}{dy}$, we have
$-x\frac{dx}{dy}+y=0$
$\Rightarrow ydy-xdx=0$
Integrating, we have
$x^2-y^2=k^2$
where $k$ is the parameter which represent family of hyperbolas.