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1. By eliminating the parameter t from the following parametric equations, find an equa- tion in terms of x and y only whose graph is the same as the parametric curve. In each case, decide if there are are any restrictions on the x and y coordinates. (a) x = t³ +t, y=t+2, (t ≤R). (b) x = Vt, yt, (te R). (c) x = cos 2t, y = = cos² t, (0 ≤ t ≤ π).

1. By eliminating the parameter t from the following parametric equations, find an equa- tion in terms of x and y only whose graph is the same as the parametric curve. In each case, decide if there are are any restrictions on the x and y coordinates. (a) x = t³ +t, y=t+2, (t ≤R). (b) x = Vt, yt, (te R). (c) x = cos 2t, y = = cos² t, (0 ≤ t ≤ π).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 36E
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1. By eliminating the parameter t from the following parametric equations, find an equa- tion in terms of x and y only whose graph is the same as the parametric curve. In each case, decide if there are are any restrictions on the x and y coordinates. (a) x = t³ + t, (b)x=t, y = √t, (t = R). (c) x = cos 2t, y = = Y t + 2, (t ≤ R). cos² t, (0 ≤ t ≤ π).
Transcribed Image Text:1. By eliminating the parameter t from the following parametric equations, find an equa- tion in terms of x and y only whose graph is the same as the parametric curve. In each case, decide if there are are any restrictions on the x and y coordinates. (a) x = t³ + t, (b)x=t, y = √t, (t = R). (c) x = cos 2t, y = = Y t + 2, (t ≤ R). cos² t, (0 ≤ t ≤ π).
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