Question

3. a) (12,5 point) What is the definitions of cone and cylinder surfaces. Write the vectoral and parametric equations of them with their figures. b) (12,5 point) Identify and construct the surface whose equation is ra+yz = 0. Cone or cylinder surface.

Answer 1

HIS 99 P.N. 1 [A Solution Coneit A surface genesated by a Speight line passing through a fixed point and Intersecting a Given curve is called a Cone. The Fixed point is called vertex of the Cone, and given curve called guiding curve. A line which generate the one is called Generator Vectoral Equation of Cone: añ slant height = 1 So can r of Cone is o r. r = 18 1 lnlcasco -> ron Koso K, Eło, 13 o semi vecter Angle Parametric Equation of lone. 2 z² = x² + y² 2 x = roso У y = rsino Z - Х CYLINDER A Surface generated by a a Speight line, which always Remains parallel to the given fixed line and which intersects to the giren Curre is called cylinder. a

His 99 P.N. 2 2 parametric ean of Cylinder 2 [x²+y? = 22 - y x=8 Cosco y = rsino q ya co 70(7,0, 2) y X vectoral egn of cylinder r= (x2442 0 = tein-'( %) Z=2 J d 1 + 0 + 2 / 2 r في [B] x²xyz =0 given equation Include 3-D Coordinate genesally we know one in the 2-D format and in 3D format cylinder is possible so x² + y2=0 cylinder equation