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

Question

(a) Eliminate the parameter to find a Cartesian equation of the curve.
(b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Answer 1

Step 1:

(a) The equations are and .

Equation of the curve .

Step 2:

(b)

Since and ,

, hence the -values in the interval .

The direction of the curve will move toward the point , but it will not reach the point.

Plot the graph From to . Use open circle for .

Solution:

(a) Equation of the curve is .

(b)

.