Parametric Equations


the conic sections, the circle, the ellipse, the parabola and the hyperbola are not functions.

the equations of the conic sections are often written as implicit relations, where y is not the subject, and this makes them difficult to deal with, especially when it comes to calculus and differentiation.

to get around this difficulty, a method called parametric equations are used.

the x and y variables are each expressed in a much simpler way in terms of a third variable. t or θ are often used. these two equations are functions.

Key Skills

find equations of conic sections from given conditions using both the cartesian (x, y) and parametric forms.


parametric equation, implicit functionconic sections, hyperbolaellipseparabola