Famous Curves Drawn from Parametric Representation

 Construct the tangent of the ellipse from its parametric representation x = a cos t y = b sin t
 Construct the tangent of the hyperbola from its parametric representation x = a sec t y = b tan t
 Construct the tangent of the Bullet's Nose from its parametric representation x = a cos t y = b cot t
 Construct the tangent of the Cross Curve from its parametric representation x = a sec t y = b csc t
 Construct the tangent of the Bowditch Curve from its parametric representation x = cos 3 t y = sin 4 t
 Construct the tangent of the graph of the Chebyshev Polynomial from its parametric representationx = cos  t y = cos 3 t
 Construct the tangent of the Lemniscate of Gerono from its parametric representationx = cos  t y = sin t cos t
 Construct the tangent of the Witch of Agnesi from its parametric representation x = tan  t y = cos 2 t
 The inverse of the hyperbola is known as the lemniscate.  Construct its tangent.
 Construct the tangent of the folium of Descartes given byx 3 + y 3 - 3xy = 0