If the tangent to a curve at a point
Question:

If the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes, then write the value of

$\frac{d y}{d x}$.

Solution:

Given that the tangent to a curve at a point $(x, y)$ is equally inclined to the coordinate axes.

$\Rightarrow$ The angle made by the tangent with the axes can be $\pm 45^{\circ} .$

$\therefore$ Slope of the tangent $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan \pm 45^{\circ}=\pm 1$