Answer to Question #93968 in Differential Geometry | Topology for Prashant

Question

Trace the curve (x/a)^2/3 + (x/a) ^2/3=1

Answer 1

The curve equation can be transformed as follows:

$$(\frac{x}{a})^{2/3}+(\frac{x}{a})^{2/3}=1$$ $$(\frac{x}{a})^{2/3}=\frac{1}{2}$$ $$\frac{x}{a}=(\frac{1}{2})^{3/2}$$ $$x=a(\frac{1}{2})^{3/2}$$

This equation represents vertical line, at $x=\frac{a}{2^{3/2}}=const$.

The line is vertical as it is independent of $y$

As an example, the plot for $a=1$ is attached