Question Solved1 Answer 17. Find a parametric representation r(u, v) for each of the following surfaces and then find a normal to the surface (a) Plane 4.r – 2y + 10% = 16. y? 22 (b) Ellipsoid x² + + = 1. 4 9 (c) Parabolic cylinder z = 3yº. Hint: It may help to read this as z = 0x + 3y2. (d) Elliptic cone z = V9x2 + y2

NUODK6 The Asker · Advanced Mathematics

Transcribed Image Text: 17. Find a parametric representation r(u, v) for each of the following surfaces and then find a normal to the surface (a) Plane 4.r – 2y + 10% = 16. y? 22 (b) Ellipsoid x² + + = 1. 4 9 (c) Parabolic cylinder z = 3yº. Hint: It may help to read this as z = 0x + 3y2. (d) Elliptic cone z = V9x2 + y2
More
Transcribed Image Text: 17. Find a parametric representation r(u, v) for each of the following surfaces and then find a normal to the surface (a) Plane 4.r – 2y + 10% = 16. y? 22 (b) Ellipsoid x² + + = 1. 4 9 (c) Parabolic cylinder z = 3yº. Hint: It may help to read this as z = 0x + 3y2. (d) Elliptic cone z = V9x2 + y2
See Answer
Add Answer +20 Points
Community Answer
6MJ9JW The First Answerer
See all the answers with 1 Unlock
Get 4 Free Unlocks by registration

Solution -: To find a parametric representation bar(gamma)(u,v) for the given following surfacesand then finding to a hornd vector to the suiface(a) Plahe quad4x-2y+10 z=16Let x=4,y=vthen z=(16-44 t2v)/(10)Hence bar(gamma)(u,v)=(:u,v,(16-4u+2v)/(10):)Now for Normal vector to the given susface(affer parametrization) is given bybar(h)= bar(gamma)_(u xx bar(gamma))quad(1 bar(gamma)_(1):}" (ross product of "{:[ bar(gamma)_(u)=(:1,0,-(4)/(10):)],[ bar(gamma)_(v)=(:0,1,(2)/(10):)],[ bar(h)= bar(gamma)_(u)xx bar(gamma)_(v)=(:0-(i*(-(4)/(10)),0-(2)/(10),1-0:):}],[ bar(h)= bar(gamma)_(u xx)xx bar(gamma)_(v)=(:4//10,-(2)/(10),1:)]:}Hence (:(4)/(10),-(2)/(10),1) is nornal vector to the plaue(c) Parabolic cylinder z=3y^(2)=0.x+3y^(2) Let x=u,y=v{:[" then "z=3v^(2)],[" lie " b ... See the full answer