Identify the surface defined by the following equation. 2² 25 -x² - y² + + 8x - 10y = 45 Select the correct choice below and fill in the answer boxes to complete your choice. A. The surface defined by the equation is an elliptic cone centered at (..) and whose traces in planes parallel to the xy-plane are ellipses. B. The surface defined by the equation is a hyperboloid of two sheets centered at (.. and whose traces in planes parallel to the xy-plane are ellipses. The shortest distance between the two sheets is C. The surface defined by the equation is an ellipsoid centered at (\.\.) that has length in the x-direction, in the y-direction, and in the z-direction. D. The surface defined by the equation is a hyperboloid of one sheet centered at (..) and is centered around the z-axis. In the xy-plane, the trace has length in the x-direction and length in the y-direction.

Consider the following equation of a quadric surface. x² v² ₂² + 441 441 441 = 1 a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Sketch a graph of the surface. a. Find the x-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The x-intercept(s) is/are located at x = (Use a comma to separate answers as needed.) B. There are no x-intercepts.

Consider the following equation of a quadric surface. y² = z² X 100 25 + a. Find the intercepts with the three coordinate axes, if they exist. b. Find the equations of the xy-, xz-, and yz-traces, if they exist. c. Identify and sketch a graph of the surface. A. The surface intersects the x-axis at x = 0. (Use a comma to separate answers as needed.) B. There are no x-intercepts. Find the y-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the y-axis at y = 0. (Use a comma to separate answers as needed.) B. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice and fill in any answer boxes within your choice. A. The surface intersects the z-axis at z = 0 . (Use a comma to separate answers as needed.) B. There are no z-intercepts. b. Find the equation of the xy-trace, if it exists. Select the correct choice and fill in any answer boxes within your choice. The trace is not a…

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