Eliminate the parameter to find a Cartesian equation of the curve.

Question

(a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.
(b) Eliminate the parameter to find a Cartesian equation of the curve.

Answer 1

(a)

Step 1:

The parametric equation are over the interval .

Observe that .

So .

Construct a table with different values of .

 

Answer 2

Contd....

Step 2:

Now plot the graph for parametric equation over .

Indicate the obtained points on the graph.

Based on the values of , indicate the direction of as it increases with an arrow.

Solution:

Answer 3

(b)

Step 1:

The parametric equation are over the interval .

Let us take .

Substitute in .

.

So the Cartesian equation is .

Solution:

The Cartesian equation is.