The explicit form of a equation is when the variables are expressed in terms of one another, such as y = mx + b. The parametric form, on the other hand, represents the variables as separate functions of a parameter, usually denoted by t.
Explicit form is typically used when the relationship between the variables is clear and easy to express in terms of one another. Parametric form is useful when the relationship is more complex and needs to be broken down into separate functions.
To convert from explicit form to parametric form, you need to solve for one variable in terms of the other, and then express both variables as separate functions of a parameter. For example, in the equation y = mx + b, you can solve for x as x = (y-b)/m, and then express both x and y as functions of t, such as x(t) and y(t).
Parametric form allows for more flexibility in representing complex relationships between variables. It also allows for the use of trigonometric functions to represent curves and other geometric shapes, making it useful in fields such as physics and engineering.
Yes, it is possible to convert from parametric form back to explicit form by eliminating the parameter t and solving for one variable in terms of the other. However, this process can be more complex and may result in multiple solutions or the need for approximations.