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Consider the path c : [0, n²] → R³ given by c(t) = (6cos"(Vi), 1 – 5sin(2Vf), 8sin*(Vi) %3D (a) Show that the curve of c lies on some plane and find the equation of the plane that contains the curve. (b) Find a point P = (xo, Yo, 20) and a positive constant r > 0 such that || c(t) – P|| = r for all t, i.e. show that the curve of c is a circle of radius r -

Consider the path c : [0, n²] → R³ given by c(t) = (6cos"(Vi), 1 – 5sin(2Vf), 8sin*(Vi) %3D (a) Show that the curve of c lies on some plane and find the equation of the plane that contains the curve. (b) Find a point P = (xo, Yo, 20) and a positive constant r > 0 such that || c(t) – P|| = r for all t, i.e. show that the curve of c is a circle of radius r -

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 61E
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Consider the path c : [0, n²] –→ R³ given by e(t) = (6cos"(V), 1 – 5sin(2V1), 8sin*(Vi) (a) Show that the curve of c lies on some plane and find the equation of the plane that contains the curve. (b) Find a point P = (x0, Yo, zo) and a positive constant r > 0 such that || c(t) – P|| = r for all t, i.e. show that the curve of c is a circle of radius r centered at P. Hint: Part (a) and part (d) might be useful.
Transcribed Image Text:Consider the path c : [0, n²] –→ R³ given by e(t) = (6cos"(V), 1 – 5sin(2V1), 8sin*(Vi) (a) Show that the curve of c lies on some plane and find the equation of the plane that contains the curve. (b) Find a point P = (x0, Yo, zo) and a positive constant r > 0 such that || c(t) – P|| = r for all t, i.e. show that the curve of c is a circle of radius r centered at P. Hint: Part (a) and part (d) might be useful.
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