# Working with parametric equations Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation. x= -7 cos 2t, y= -7 sin 2t, 0 leq t leq pi

Chardonnay Felix 2021-02-21 Answered
Working with parametric equations Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x and y. b. Describe the curve and indicate the positive orientation.
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Step 1 Given: The following parametric equations,

Step 2 a) To eliminate the parameter to obtain an equation in x and y. We have, The following parametric equations, (1)
(2) Adding equations (1) and (2), we get

$=49$ An equation in x and y is Step 3 b) To describe the curve and indicate the positive orientation. We have, The curve represents a circle at the origin, To indicate the positive orientation, we will use the following parametric equations, The interval given is

Implies the initial point is For $t=\pi ,$
Implies the end point is The initial point and the end point are equal, that is, Hence, the orientation is positive in anticlockwise direction.