Mathematical name of time dilation curve

[HALON]

In mathematics, what is the name (type) for a curve given by velocity and time dilation?

Specifically, I want to find a name for the curve y=1/(1-x^2)^{1/2}

This curve is derived from the equation of a unit circle (x-a)^2+(y-b)^2=r^2
where y=(1-x^2)^{1/2}

 

[Simon Bridge]

It's called a hyperbola. Well - sort of.

The general equation is: $(x^2-h)(y^2-k)=m$

Your relation has $k=0, h=-1, m=-1$

This is a rectangular hyperbola in $(x^2,y^2)$

You can get much more general than that by just taking the product of two polynomials... $$P_n(x)P_m(y)=\text{const.}$$