How do i write parametric equations?
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x=f(t), y=g(t), z=h(t), etc., where f, g and h are (usually different) functions of t, where t is the parameter. There can be as many variables (x, y, z, etc.) as necessary representing multidimensional space. 3 is usually the maximum and 2 the minimum number of variables. Because each variable can be expressed in terms of a common variable t, it is possible to find, for example, an equation between y and x by eliminating t between their parametric equations. For example, if y=t+1 and x=t^2-1, t=y-1 and this can be substituted in the second equation to relate x and y: x=(y-1)^2-1=y^2-2y. So y^2-2y-x=0 can be plotted as a graph. Also, dy/dx can be found by calculating dy/dt and dx/dt and then dividing one by the other: dy/dx=(dy/dx)/(dx/dt). (x,y) would be represented by (t^2-1,t+1). Sometimes it's easier and less complicated to express parametrically than to express, say, y in terms of x.

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