Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis. Equation of Curve z2 = 16y Coordinate Plane Axis of Revolution yz-plane y-axis
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis.Equation of Curvez2=4yCoordinate Planeyz-planeAxis of Revolutiony-axisFind an equation of the surface of revolution obtained by revolving the plane curve 4x² – y² = 4 about the x-axis. Name the surface.
- find an equation of the surface of revolution generated by revolving curve equation of curve coordinate plane axis of revolution z=5y yz-plane z-axisFind an equation of the surface of revolution generated by revolving the plane curve about the indicated axis. Draw a sketch of the surface. c. x2 + 4z2 = 16 ; about the x-axisHow would I solve this problem? Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis. Equation of Curve: z^2=64y Coordinate Plane: yz-plane Axis of Revolution: y-axis
- Find the equation of the surface of revolution that is generated by rotating the straight line y = x around the y-axis. Is it a quadric surface? What name can be given to it?The 2D curve 4x2 - y2 = 3, generates a surface in 3D by rotationing it out of the xy-plane and around the x-axis. Create the equation for the surface. A)If the resulting equation does not qualify as a quadric surface based on the general definition, explain in a few clearly written sentences, why it does not and you are done. B) If the resulting equation qualifies as a quadric surface, write the equation in standard form, state the exact name and identify the constants a, b and c as needed.Find the lines curvatures, the first and second fundamental forms of the surface: the surface
- Find an equation of the surface of revolution generated by revolving the plane curve about the indicated axis. Draw a sketch of the surface. b. y2 = z3 ; about the z-axisMatch the equation with the surface it defines. Identify the surface by type (paraboloid, ellipsoid, etc.). 3x2+3z2 = 54. Choose the correct graph of the equation below.Also need to know what surface it is?