Circles and arcs Eliminate the parameter to find a description of the following circles or circular arcs in terms of x and y. Give the center and radius, and indicate the positive orientation.

x = 3 cos t, y = 3 sin t; 0 ≤ t ≤ π/2

Solution 16E

Step 1:

In this problem we have to eliminate the parameter o find a description of the following circles or circular arcs in terms of x and y.

Given

This is very similar to the circle of radius 3.

Now suppose we plug in these parametric equations to we get

(since

Thus

This is a circle of radius 3, centered at (0, 0).