VECTORS AND THE GEOMETRY OF SPACE 12.6 Cylinders and Quadric Surfaces 1 Lecture’s outline 2 Elliptical Cylinders Circle or Cylinder? Graph π₯! + π¦! = 4 3 Elliptical Cylinders (Cont’d) Elliptical cylinder along the z-axis π₯! π¦! + !=1 ! π π π π 4 Elliptical Cylinders (Cont’d) Elliptical cylinder along the y-axis ! π ! π₯ π§ + !=1 ! π π Since π is missing, the cylinder is along the y-axis. π 5 Elliptical Cylinders (Cont’d) Since π is missing, the cylinder is along the x-axis. Elliptical cylinder along the x-axis π¦! π§! + !=1 ! π π π π 6 Elliptical Cylinders (Cont’d) Graph in 3D πππ£πππ ππ¦ 36: 4π₯ ! + π¦ ! = 36 Since π is missing, the cylinder is along the z-axis. π₯! π¦! + =1 9 36 π = 3, π=6 πΈπππππ‘ππππ ππ¦ππππππ πππππ π‘βπ π§ − ππ₯ππ 7 Elliptical Cylinders (Cont’d) Graph in 3D π₯ ! + 4π§ ! = 16 πππ£πππ ππ¦ 16: Since π is missing, the cylinder is along the y-axis. π₯! π§! + =1 16 4 π = 4, π=2 πΈπππππ‘ππππ ππ¦ππππππ πππππ π‘βπ π¦ − ππ₯ππ 8 Elliptical Cylinders (Cont’d) Graph in 3D Since π is missing, the cylinder is along the z-axis. π₯ ! + (π¦ − 1)!= 1 π₯ ! + (π¦ − 1)!= 1, π§=0 ππππππ ππ ππππ‘ππ 0,1,0 πππ πππππ’π 1 ππ π‘βπ π₯π¦ − πππππ πΆππππ’πππ ππ¦ππππππ πππππ π‘βπ π§ − ππ₯ππ 9
