Describing a circle Find a pair of equations describing a circle of radius 3 centered at (2, 4, 1) that lies in a plane parallel to the xz-plane.
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Describing a circle Find a pair of equations describing a circle of radius 3 centered at (2, 4, 1) that lies in a plane parallel to the xz-plane.
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- Distance from a point to a plane Find the distance from the point (2, 2, 2) to the plane x + 2y + 2z = 1.Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. x2+y2+(z+8)2=100, and z=−2 Choose the correct description from the options below. (Explain) The circle with center (0,0,-2) and radius 64, parallel to the xy-plane The line through (8,0,-2) and (0,8,-2) The line through (8,8,-2) parallel to the z-axis The circle with center (0,0,-2) and radius 8, parallel to the xy-planeIdentifying surfaces Identify the following surfaces by name. y = 4z2 - x2
- Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations). z = 4 - 2x2 - y2; (2, 2, -8) and (-1, -1, 1)Tangent planes Find an equation of the plane tangent to the following surfaces at the given points (two planes and two equations). yzexz - 8 = 0; (0, 2, 4) and (0, -8, -1)Tangent planes Find an equation of the plane tangent to the following surfaces at the given points. x2 - 2x + y2 + 4y + 3z2 = 2; (3, -2, 1) and (-1, -2, 1)
- equation of planeArea of Surface Revolution Find the area of the surface of revolution generated when the given curve is revolved about the indicated axis.Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. x2+y2=36, z=3 Choose the correct description. A. The circle with center (6,6,0) and radius 3, parallel to the xy-plane B. The circle with center (0,0,3) and radius 6, parallel to the xy-plane C. The line through (6,6,3), parallel to the z-axis D. The line that passes through the points (6,0,3) and (0,6,3)