Question 2 (a) Show that the following set is a curve: K = {(x, y) E R² | xy – x = 1}. Briefly explain your reasoning. (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y? = 1}, that generates the clockwise orientation of C. Be sure to specify the domain. (c) Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y = x²} at the point (-2,4).

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 31E
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Question 2
(a) Show that the following set is a curve:
K = {(x, y) E R² | xy – x = 1}.
Briefly explain your reasoning.
(b) Give an example of a parametrisation of the unit circle,
C = {(x, y) E R² | x² + y? = 1},
that generates the clockwise orientation of C. Be sure to specify the domain.
(c) Find the rightward-pointing (positive x-direction) unit tangent to the curve
P = {(x, y) E R² |y = x²}
at the point (-2,4).
Transcribed Image Text:Question 2 (a) Show that the following set is a curve: K = {(x, y) E R² | xy – x = 1}. Briefly explain your reasoning. (b) Give an example of a parametrisation of the unit circle, C = {(x, y) E R² | x² + y? = 1}, that generates the clockwise orientation of C. Be sure to specify the domain. (c) Find the rightward-pointing (positive x-direction) unit tangent to the curve P = {(x, y) E R² |y = x²} at the point (-2,4).
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