A parametric equation is a set of equations that express a set of quantities as a function of one or more independent variables, known as parameters. These equations are commonly used to represent curves and surfaces in mathematics and physics.
A regular equation typically has one dependent variable and can be solved for that variable in terms of the independent variable. A parametric equation, on the other hand, has multiple dependent variables and cannot be solved for any one variable in terms of the independent variable. Instead, the dependent variables are expressed as functions of the independent variable.
Parametric equations are commonly used in physics, engineering, and computer graphics to model and analyze motion, curves, and surfaces. They are also used in economics and finance to represent complex relationships between variables.
Parametric equations are typically graphed by plotting points on a coordinate plane using the parameter as the input and the dependent variables as the output. These points are then connected to create a curve or surface. Alternatively, parametric equations can be graphed using a parametric graphing calculator or software.
Parametric equations provide a more versatile and flexible way of representing curves and surfaces, compared to regular equations. They allow for the inclusion of multiple variables and can easily handle complex relationships between them. Additionally, parametric equations are often easier to manipulate and analyze than regular equations.