Parametric equations

Equations in analytic geometry correspond to the surfaces and curves. A typical curve is described by the function which generates a value on the y-axis from every value on x-axis. A typical surface is described by a function that generates a value on z-axis from every pair of x-y coordinates. Kinematics equations are described in a way that is rather different. The position of the moving object changes along with time. Because the x, y, and z values depend on an additional parameter that is not a part of the coordinate system, kinematics equations are also known as parametric equations. According to Einstein the universe is not three-dimensional with three coordinates - x, y, and z - it's 4-dimensional with 4 coordinates - x, y, z, and t. Objects appear to us to move just because we are swept up in the flow of time. If we could see time the same way we see length then objects in motion would appear as rigid curves fixed in the space - a 4-dimensional space which included time, called as space-time. In the sense, relativity abolished the motion.

Since all perpendicular directions are orthogonal and since any vector quantity can be resolved into components along these directions, n-dimensional motion can be described by n one-dimensional algebraic expressions completely in n perpendicular directions (where n is any whole number greater than zero). Therefore 2-dimensional motion can be completely described by two 1-dimensional algebraic expressions along two perpendicular directions - generally called as x and y.

Given a function F which consists of X and Y parametric equations, each of them expressed as a function of the same independent variable t.
Generally it is difficult for students to imagine the graph of F.
By using the Applet of Parametric Equations, graph of F can display and visual explanation for table of derivatives of X and Y can be given. Parametric Equations in plane is a pair of functions

x = f(t) and y = g(t)

which describe x and y coordinates of graph of some curve in plane.

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