This demo shows the graph of x(t),y(t).

In the graph labeled t,x(t), there are two blue lines through a point (t0, x(t0), one with a slope ε greater than that of the tangent line and one with a slope ε less than that of the tangent line, while in the graph labeled t,y(t), there are two green lines through a point (t0, y(t0), one with a slope ε greater than that of the tangent line and one with a slope ε less than that of the tangent line.  If the curve is differentiable at t0, you should always be able to choose a δ small enough that the portion of the curves t,x(t) and t,y(t) between t0 - δ and t0 + δ lies inside the blue and yellow lines respectively.