Consider x² 441 the following equation of a quadric surface. y² z² 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. A. The x-intercept(s) is/are located at x = -21,21. (Use a comma to separate answers as needed.) OB. There are no x-intercepts. C Find the y-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) is/are located at y = 21, -21. (Use a comma to separate answers as needed.) OB. There are no y-intercepts. Find the z-intercepts, if they exist. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The z-intercept(s) is/are located at z = (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 below and, if necessary, fill in the answer box to complete your choice. OA. The trace is not a single point. The equation of the xy-trace is OB. The trace is a single point (... O c. There is no xy-trace.

Determine the scaler equation of a plane that contains the point (3, 1, -2) and Y-axis.

Identify the quadric surface for the equation y² - x² = 16. a parabolic cylinder a hyperbolic paraboloid an elliptic cylinder a hyperboloid of two sheets a hyperbolic cylinder Determine the intercepts of the quadric surface. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer in the form of a comma-separated list of point coordinates in the form (*, *, *). Enter DNE if the surface and the axes does not intersect.) intercept(s): (0,0,0) Incorrect Determine the traces of the quadric surface. (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the surface and the plane are not traced. If a trace of the surface in the plane is a point, give your answer as point coordinates in the form (*, *, *).) the trace in the xy-plane: Incorrect the trace in the xz-plane: Incorrect the trace in the yz-plane: Incorrect

For each equation from 1-8, use a graphing utility to sketch and describe the surface. 1. y=7 2. z -5

Write the equation and determine the type of surface obtained by rotating this line around the specified coordinate axis, make a picture:4x2-3y2=12, Ox