The curve for which slope of the tangent at any point equals the ratio of the abscissa to the ordinate of the point is a/an

ellipse rectangular hyperbola circle parabola

rectangular hyperbola

$\frac{d y}{d x}=\frac{x}{y} \Rightarrow ydy=xdx$ $\Rightarrow \frac{y^2}{2}-\frac{x^2}{2}=c \Rightarrow y^2-x^2=2 c$ which is a rectangular hyperbola Hence (2) is the correct answer.