(a) x² + 2x + 4y² + 16y + 9z? 19

. Eliminate the parameter to find the standard form gedaa rectangular equation representing the graph of x = 3 cot t + 1 y = 2 csc t -- 2. Show your work by hand.

In the main lobby of the hotel, there is a circular hospitality area that also rotates. The radius of the hospitality area is 3 m. The distance from the front door, at point A, to the far side of the hospitality area, at point C, is 20 m. At a certain moment the dessert bar is located at point B and the tourist information desk is located at point E. B E 6. Assuming AB and AE are tangent to the circle, find CD and AD. Explain how you arrived at your answers.

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.