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 representation

x = cos  t

y = cos 3 t

Construct the tangent of the Lemniscate of Gerono from its parametric representation

x = 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 by

x 3 + y 3 - 3xy = 0