For $f(x,y)=x^{2}-y^{2}$, determine the shape of the parametric curve.

Question

For $f(x,y)=x^{2}-y^{2}$, $\mathbf{c}=(0,0)$, determine the shape of the parametric curve $\mathbf{F}(t)=\mathbf{f}(\mathbf{c}+t\mathbf{u})$ for $\mathbf{u}=(1,0)$.

I am not sure if my attempt is correct, but all I did was $\mathbf{F}(t)=\mathbf{f}((0,0)+t(1,0))=\mathbf{f}(t,0)=t^{2}$. So then the parametric curve is just a parabola?

Answer 1

Yes, your attempt is correct. The parametric curve is a parabola.