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  • The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is (a) an ellipse (b) parabola (c) circle (d) rectangular hyperbola

The curve for which the slope of the tangent at any point is equal to the ratio of the abscissa to the ordinate of the point is
(a) an ellipse      (b) parabola   (c) circle         (d) rectangular hyperbola

Answers (1)

The answer is the option (d) Rectangular Hyperbola

Explanation: -

According to the question, \frac{d y}{d x}=\frac{x}{y}$ $\Rightarrow \quad y d y=x d x$
On integrating both sides, we get
$$ \frac{y^{2}}{2}=\frac{x^{2}}{2}+C $$
\Rightarrow \quad y^{2}-x^{2}=2 C,$ which is an equation of rectangular hyperbola.

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