Question

Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of the curve.

Answer 1

Step 1:

(a)

The parametric equations are and and interval of the graph is .

Construct a table for different values of t.

Graph:

Draw the coordinate plane.

Plot the point obtained from the table.

Connect the points to a smooth curve.

Observe the graph:

From  to , the ellipse completes it first revolution in anti-clockwise.

Step 2:

The parametric equations are and .

Consider .

Consider .

Trigonometric identity : .

Rectangular equation of the curve is .

Solution:

Graph of the curve is

Rectangular equation of the curve is .