If we consider an object having a curvilinear motion in any given direction and at any instance of time. “If x and y are continuous functions of t in any given interval, then the equationsĪre called parametric equations, and t is called an independent parameter.” Hence, parametric equations can be more particularly defined as: Similarly, it can also help us detect the earth’s movement with respect to time. Hence, in this case, we will use x(t) and y(t) as variables, where t is the independent variable, to determine the position of the earth in its orbit. So, then parametric equations come into play as only one variable can be solved at a time. Now, a question arises how we can write and solve the equations for describing the position of the earth when all the other parameters such as the speed of the earth in its orbit, distance from the sun, distance from other planets revolving in their particular orbits and many other factors, all are unknown. At any instance, the earth is at some particular position relative to the other planets and sun. To have a better understanding, let’s consider an example of our planetary system as the earth revolves around the sun in its orbit with some speed.
Parametric equations are useful for representing and explaining curves such as circles, parabolas, etc., surfaces, and projectile motions.
The method of forming parametric equations is known as parameterization. Similarly, parametric equations are not necessarily functions. It is important to note that parametric equation representations are not unique hence, the same quantities can be expressed in several ways. There can be more than when dependent variables, but they do not depend on each other. Understanding with the help of examples.Ī parametric equation is a form of the equation that has an independent variable called a parameter, and other variables are dependent on it.
Parametric equations on graphmatica how to#
How to graph various parametric equations?.In this topic, we will cover the following points in detail: Where “t” is an independent variable called a parameter. Instead of writing it in the cartesian form that is y = x 2 we can write it in parametric form, which is stated as follow, “A form of the equation that has an independent variable in terms of which any other equation is defined, and dependent variables involved in such an equation are continuous functions of the independent parameter.”įor instance, let us consider the equation of a parabola. In mathematics, a parametric equation is explained as: Parametric Equation – Explanation and Examples
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