How to know the shape of the parametric curve $(\frac{6m^2 - 8m}{m^2+1}, \frac{-6m + 8}{m^2 + 1})$?

Question

How to know the shape of the parametric curve $(\frac{6m^2 - 8m}{m^2+1}, \frac{-6m + 8}{m^2 + 1})$, where $m$ goes from -$\infty$ to $\infty$?

I know it should be a circle by plotting it on a graph using a computer, but does there exist a mathematical way for me to deduce the shape of this parametric curve? Obviously, $x = -my$ here but I don't see how it gives useful information.

Answer 1

Consider $$\frac{x}{y}=-m$$ Substitute this expression for $-m$ into the expression for $y$ and you end up with the equation of a circle.

Can you finish?