Find the vector equation that represents the curve of intersection of the paraboloid z=4x2+y2\displaystyle {z}={4}{x}^{{2}}+{y}^{{2}} and the surface y=x5\displaystyle {y}={x}^{{{5}}}.

Write the equation so that one of the functions is simply t\displaystyle {t}.

x(t)=\displaystyle {x}{\left({t}\right)}=  
y(t)=\displaystyle {y}{\left({t}\right)}=  
z(t)=\displaystyle {z}{\left({t}\right)}=