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 = 36y 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 for the surface consisting of all points that are equidistant from the point (0,0,1) and the plane z=−1. Identify 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. c. x2 + 4z2 = 16 ; about the x-axis
- 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.How 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-axisFind 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?
- Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis.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-axisFind the lines curvatures, the first and second fundamental forms of the surface: the surface