solve the question (b) Differential Geometry Question:2. A surface S in R"(r, y, 2) is defined parametrically in the formu + p2 -u2 + p2 +1' u² + v² + I' u² + p2 +2vX(u, v) =(a) Find points on the surface S such that the tangent plane to S at these points isparallel to the plane r+y =0.(b) Calculate the first fundamental form of the surface S.(c) Calculate the area of the region on the surface S specified by the inequalityu? + v? < a?, a = const.

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Answered: 2. A surface S in R'(z,y, =) is defined…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 5ECP: Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle...

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2. A surface S in R'(z,y, =) is defined parametrically in the form u + -1 -( ) X(u, e) = 2u 2 (a) Find points on the surface S such that the tangent plane to S at these points is parallel to the plane r+y= 0. (b) Calculate the first fundamental form of the surface S.