The paraboloid described by the equation x² + y2 - z = 0 and the plane described by the equation 2x - 4y -z = 4 intersect to form the curve C. (a) Show that the curve C lies on the cylinder described by the equation (x - 1)² + (y + 2)² = 1. Hint: Eliminate z. (b) State a parametrisation of the curve C. (c) Find a unit tangent vector to the curve C at the point P: (x, y, z) = (2, -2,8).
The paraboloid described by the equation x² + y2 - z = 0 and the plane described by the equation 2x - 4y -z = 4 intersect to form the curve C. (a) Show that the curve C lies on the cylinder described by the equation (x - 1)² + (y + 2)² = 1. Hint: Eliminate z. (b) State a parametrisation of the curve C. (c) Find a unit tangent vector to the curve C at the point P: (x, y, z) = (2, -2,8).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 17T
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