Parametric Equations

In plane, parametric equation is a pair of Functions which is given by:
⇒x = f (s) and y = g (s); which is used to define the ‘x’ and ‘y’ coordinate graph of the given curve in the plane.
In mathematics, a Set of equations which is used to represent a set of quantities as unambiguous Functions of a number of independent variables, said to be parameters.
For example, Circle equation in the Cartesian coordinate is given by:
r² = x² + y², and Circle equation for the Parametric Equations is given by:
⇒x = r cos s;
⇒y = r sin s;
Basically the parametric equation is represented as non unique, so the same quantities are defined by number of different parameterizations. Now we will see two dimensional and three dimensional parametric equations.
In the two dimensional parametric equations Parabola and circle are involved.
Parabola: The equation of parabola is given by:
⇒y = x²;
The given equation is parameterising using the other parameter, when we use another parameter then the equation of parabola is:
⇒x = s and,
⇒y = s².
In case of circle, the ordinary Equation of Circle is given by:
⇒x²+ y² = 1;
Here we obtained the equation which is parameterized.
Using the parameterize version it is very easy to get points on a plot. Let’s talk about the three dimensional parametric equations. ‘Helix’ include in the three dimensional parametric equation.
Generally parametric equation is used to define the curve in higher- dimensional space.
For example: x = a cos (s),
⇒y = a sin (s);
⇒z = bs;
Given equation defines a three dimensional curve, the radius of Helix ‘a’ and riser to 2b unit per turn.