11-14 Describe in words the surface whose equation is given. 11. 0 — п/4 12. r = 5 13. ф T/3 14. р — 3
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14) I would need some help with "describe in words the surface whose equation is given" for question #14, please?
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- 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?Let S be the surface with equation 4y2 + 4z2 - x2 - 16 = 01) Find an equation of a generating curve on the xz-plane if S is viewed as a surface of revolution.Please write answers and solutions paper, do not just type them.Please answer and show the complete solution for Item IV.Let S be the surface with equation given by 4x2- 9y2 = 9(z2 + 4).I. Find an equation of the trace of S on each of the coordinate planes and on the planes x = ±3√ 2. Determine if each trace is empty, a point, a (pair of) line(s), a parabola, an ellipse, or a hyperbola.II. What type of quadric surface is S?III. Using the traces obtained in I, provide a hand-drawn sketch of S. Label all important points (e.g. vertices) found on each trace.IV. View S as a surface of revolution. Find an equation of a generating curve on the xy-plane which, if revolved about the x-axis, will result to S.
- 8.2) 13) Find the exact area of the surface obtained by rotating the curve about the xaxis.The surface defined by the equation z= 4x2 + y2 is called an elliptical paraboloid. a. Write the equation with x = 0. What type of curve is represented by this equation? b. Write the equation with y = 0. What type of curve is represented by this equation? c. Write the equation with z = 0. What type of curve is represented by this equation?Sketch the section of the surface at y = 0. 9x^2+4z^2=36
- explain the geometric relationship between the answer found in part b and the surface defined aboveMatch the equation with the surface it defines. Also, identify the surface by type (paraboloid, llipsoid, etc.) 4x=z2−y2 Which graph below shows the surface?A surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Make a sketch of the surface in the third dimension, marking the coordinates of the points where |x|, |y|, or |z| is maximized.