Conversion From Two Parametric Equations To A Single Equation
Converting a set of parametric equations to a single equation involves eliminating the variable from the simultaneous equations . If one of these equations can be solved for t, the expression obtained can be substituted into the other equation to obtain an equation involving x and y only. If and are rational functions then the techniques of the theory of equations such as resultants can be used to eliminate t. In some cases there is no single equation in closed form that is equivalent to the parametric equations.
To take the example of the circle of radius a above, the parametric equations
can be simply expressed in terms of x and y by way of the Pythagorean trigonometric identity:
which is easily identifiable as a type of conic section (in this case, a circle).
Read more about this topic: Parametric Equation
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