# Seeking affine reparameterization of a curve [closed]

A ray of light propagates along the straight line

$$x(p) = \frac{p}{\sqrt{3}}$$ $$y(p) = \frac{p}{\sqrt{3}}$$ $$z(p) = \frac{p}{\sqrt{3}},$$

where $$p$$ is a parameter.

Reparameterize this curve with a new parameter $$\lambda$$, where $$\lambda$$ is an affine parameter. The metric is flat, $$ds^2=dx^2+dy^2+dz^2-c^2dt^2$$

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