Sketching Curves From Parametric Equations

MathsDirect

How do you sketch the curve described by the parametric equations?

The simplest method is to eliminate the t, so that you are left with a cartesian equation.

To do this, make t the subject of one equation and then substitute this into the other equation

Now, you just need to follow the method for sketching a cartesian function.

1

		The curve crosses the axes at (0,0) and (2,0)

2	There are no assymptotes

4	Differentiate
	Therefore there is a stationary point at
	Looking either side

Summarizing the results

1	The curve cuts the axes at (0,0) and (0,2)
2	The curve goes to infinity as x goes to infinity,( plus or minus.)
3	There is a minimum at (1,-1)