Using parametric equations to define coordinates

This article explores using parametric equations to define coordinates of a point. Parametric equations can be used to define the coordinates of a point. In parametric equations the coordinates of x are expressed as x=f(t) and y expressed as y=g(t) where the variable t is a parameter.
Below are some examples.

Example

In this example we shall draw the curve given by the following parametric equations in the range -3 ≤ t ≤ 3.
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Drawing a table should help us in the finding the values of x and y. To find the values of x and y we substitute the values of t into the parametric equations x=2t and y=t² for example when t = 2;
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…and…
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Therefore when t=2 the curve passes through the point (4, 4). Draw the table in the asked range and fill in the values;
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Now we can plot the points on the graph and draw the draw the curve. The points we shall plot are; (-6, 9), (-4, 4), (-2, 1), (0, 0), (2, 1), (4, 4), (6, 9)
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Example

In this example we shall find the Cartesian equation of the curve. Below are the parametric equations;
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A Cartesian equation is an equation in terms of x and y. We must therefore eliminate t from the parametric equations x=2t and y=t ²
For the equation x=2t we shall rearrange to make t the subject.
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Now replacing t in the y equation should give the Cartesian equation;
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Therefore the Cartesian equation from the parametric equations Is;
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