(3) [Marked] Consider the surface of revolution = {(x,y (x, y, z) € R³ | x² + z² *-{\306842-({+1})} H = = cos (a) Find the tangent plane to H at (23/2,π, -23¾½). (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2, π, 2√2 (2√21π-232). (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)

Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
Question
(3) [Marked] Consider the surface of revolution
= {(x,y
(x, y, z) € R³ | x² + z²
*-{\306842-({+1})}
H =
=
cos
(a) Find the tangent plane to H at (23/2,π, -23¾½). (See also (Q7) of Problem Sheet 7.)
(b) Find the unit normals to H at (23/2, π,
2√2
(2√21π-232).
(c) Which of the two unit normals in (b) represents the "outward-facing" side of H?
(For part (c), you do not have to prove the answer. You can find the answer by sketching H
and the appropriate normals and then inspecting your sketch.)
Transcribed Image Text:(3) [Marked] Consider the surface of revolution = {(x,y (x, y, z) € R³ | x² + z² *-{\306842-({+1})} H = = cos (a) Find the tangent plane to H at (23/2,π, -23¾½). (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2, π, 2√2 (2√21π-232). (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)
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