WebJul 5, 2012 · The problem is to find the parametric equations for the ellipse which made by the intersection of a right circular cylinder of radius c with the plane which intersects the z-axis at point 'a' and the y-axis at point 'b' when t=0. I think the equation for the cylinder would be x2 + y2 = c2 As for the plane I am less sure about the equation. WebNov 16, 2024 · Section 9.5 : Surface Area with Parametric Equations. In this final section of looking at calculus applications with parametric equations we will take a look at determining the surface area of a region obtained by rotating a parametric curve about the x x or y y -axis. We will rotate the parametric curve given by, x = f (t) y =g(t) α ≤ t ≤ ...
Cylinder—Wolfram Language Documentation
WebJan 22, 2024 · Figure : In cylindrical coordinates, (a) surfaces of the form are vertical cylinders of radius , (b) surfaces of the form are half-planes at angle from the -axis, and (c) surfaces of the form are planes parallel to the -plane. Example : Converting from Cylindrical to Rectangular Coordinates WebCylinder [ { { x1, y1, z1 }, { x2, y2, z2 } }, r] represents a cylinder of radius r around the line from ( x1, y1, z1) to ( x2, y2, z2). Cylinder [ { { x1, y1, z1 }, { x2, y2, z2 } }] represents a cylinder of radius 1. Details Examples open all Basic Examples (4) A unit radius and two units height cylinder: In [1]:= Out [1]= can griffins breed
Parametric equations for cylinder/plane intersection
WebDec 28, 2024 · Converting from rectangular to parametric can be very simple: given y = f(x), the parametric equations x = t, y = f(t) produce the same graph. As an example, given y … WebI usually use the following parametric equation to find the surface area of a regular cone z = x 2 + y 2 : x = r cos θ y = r sin θ z = r And make 0 ≤ r ≤ 2 π, 0 ≤ θ ≤ 2 π. I've now have a cone z = 2 x 2 + 2 y 2 and I think the parametric equation I normally use won't work anymore. Which would be a more suitable one in this case? WebThe general parametric equations of a cylinder parameterized with cylindrical coor-dinates are 2 x =arcos(q) y=brsin(q) z=z For a circular cylinder, the equations are simply x =rcos(q) y=rsin(q) z=z 3 Graphing 3D Parametric Equations Creating a 3D Parametric graph for the first time can be somewhat confusing, so the can griffins fly in feather family