? Exercise 13.1.3The 3D model below shows the intersection of the paraboloid z =422 + y? and the parabolic cylindery = 2. Find a parameterization for this intersection curve.0.1F(t) =(Write i, j, or k for i, j, or k)• Hint

To find parametric equation of the curve obtained by intersection of below surfaces. z=4x2+y2y=x2

Answered: 4z² + y and the parabolic cylinder The…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 20T

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Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
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Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 . Locate the lowest and highest temperatures on the sphere.
a. Find a parametrization for the hyperboloid of one sheet x2 + y2 - z2 = 1 in terms of the angle u associated with the circle x2 + y2 = r2 and the hyperbolic parameter u associated with the hyperbolic function r2 - z2 = 1. (Hint: cosh2 u - sinh2 u = 1.) b. Generalize the result in part (a) to the hyperboloid (x2/a2 ) + (y2/b2 ) - (z2/c2 ) = 1.

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4z² + y and the parabolic cylinder The 3D model below shows the intersection of the paraboloid z = y = z. Find a parameterization for this intersection curve.