Question

The curve in which the slope of tangent at any point equal to the ratio of the abscissa to the oridinate of the point is

• A. an ellipse
• B. a parabola
• C. a rectangular hyperbola
• D. a circle

Answer 1

Answer: (C)

a rectangular hyperbola

Given that the slope of the tangent is equal to the ratio of the abscissa to the ordinate of the point
$\frac{dy}{dx}$ =$\frac{x}{y}$
$xdx-ydy=0$
Integrating both sides, we get
$x^2-y^2=k$, which is an equation of rectangular hyperbola.