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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).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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).
Transcribed Image Text: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).
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