In the following cylinders, determine the name of the curve through which the generatrices pass and make a sketch of the surface. 1.- z²+ y² = 36
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- Identify and sketch the surface (S) of equation z = + 16 4 your work). .(Show all the details ofFind an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis.Find an equation for the surface of revolution formed by revolving the curve 2x + 3z = 1 in the xz-plane about the x-axis.
- A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax? about the y-axis. If the dish is to have a 8-foot diameter and a maximum depth of 2 feet, find the value of a and the surface area (in square feet) of the dish. a = ft? Area =Find the points where the line y=−3xy=-3x intersects a circle of radius 2 centered at the origin. Give exact values for the x and y coordinates.Write the equation for the surface generated by the revolving curve y = 2x +1, revolved around the x and y axis. Sketch afterwards.
- Find the equation of the tangent plane to the given surface at the pointP. x2 + y2 = 4, P = (sqrt(3),0,3) Please give a full explanation to the answer.q11 a) Find the x-intercepts. 1. Find the y-intercepts. 2. Find the z-intercepts. b) Find the equation of the xy-trace. 1. Find the equation of the xz-trace. 2. Find the equation of the yz-trace. c) Sketch a graph of the surface.