Sketch the vector field.

\(\mathbf{F}(x, y)=\left\langle\frac{4 y}{\sqrt{x^{2}+4 y^{2}}}, \frac{-x}{\sqrt{x^{2}+16 y^{2}}}ightangle\)
Show that \(\mathbf{F}\) is a unit vector field tangent to the family of ellipses \(x^{2}+4 y^{2}=c^{2}\).