Slope of the normal to the curve $y = x^{2} - \frac{1}{x^{2}}$ at the point $(-1, 0)$ is:

What is the length of the sub-tangent at any point on the curve $y = ax^3$?

If $P$ and $Q$ are two different points on the curve $y = x^3 - x$ such that the tangent at $P$ intersects the curve again at $Q$,then $\frac{m_{OQ} + 1}{m_{OP} + 1}$ is equal to,where $O$ is the origin and $m_{AB}$ represents the slope of the line segment $AB$.

The angle between the tangent lines to the graph of the function $f(x) = \int_{2}^{x} (2t - 5) \, dt$ at the points where the graph cuts the $x$-axis is

The length of the subtangent at any point of the curve $x^my^n = a^{m+n}$ is proportional to

The sum of the intercepts on the coordinate axes made by the tangent to the curve $\sqrt{x} + \sqrt{y} = \sqrt{a}$ is