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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- Find an equation for the surface of revolution formed by revolving the curve in the indicated coordinate plane about the given axis.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 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 =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 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.
- 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.