6.2 Converting Parametric to Rect

Converting from Parametric Equations

to Rectangular Form

~ To change parametric equations to rectangular form, you must eliminate the parameter, t.

~ Solve one parametric equation for t.

~ Substitute the resulting expression into the other parametric equation, then simplify.

NOTE: Some equations are impossible to rewrite in terms of x - i.e.

x = y^2 - 3y + 2. This would be crazy to rewrite as y = ..., so leave equations like the above example as it is.

Example 1

Let x = 4t - 1 and y = 6 - t

We will use y = 6 - t to eliminate the parameter.

y = 6 - t

-y + 6 = t

Now replace the parameter in the equation x = 4t - 1.

x = 4(-y + 6) - 1

x = -4y + 24 - 1

x = -4y + 23

4y = -x + 23

y = -x/4 + 23/4

You will get the same answer if you eliminate the parameter using x = 4t - 1.

Using y = 6 - t is easier to use because of the coefficient of t.

Whereas, in x = 4t - 1, the coefficient of t is 4 which might result in using fractions.

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