Piecewise defined curve

The curve is given by
\( k_1(t) =( a \cos(t),\sin(t))^{\top}\),
\(k_2(t)= (a+t(b-a),0)^{\top}\),
\( k_3(t) = (-b \cos(t),b\sin(t))^{\top}\),
\( k_4 (t) = (b+t(a-b),0)^{\top}\)
with a proper choise of \(t\in\mathbb{R}\) for each curve.