The curve for which the slope of the tangent at any point is equal to the ratio of the abcissa to the ordinate of the point is

Slope of tangent to the curve $= \frac{{dy}}{{dx}}$

and ratio of abscissa to the ordinate $= \frac{x}{y}$

According to the question,

$\frac{{dy}}{{dx}} = \frac{x}{y}$

$ydy = xdx$

On integrating both sides,

we get
$\frac{{{y^2}}}{2} = \frac{{{x^2}}}{2} + C$

$\Rightarrow$ $\frac{{{y^2}}}{2} - \frac{{{x^2}}}{2} = C \Rightarrow {y^2} - {x^2} = 2C$

which is an equation of rectangular hyperbola.