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 [itex]y=1/(1-x^2)^{1/2}[/itex] This curve is derived from the equation of a unit circle [itex](x-a)^2+(y-b)^2=r^2[/itex] where [itex]y=(1-x^2)^{1/2}[/itex]
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... $$P_n(x)P_m(y)=\text{const.}$$