Parabolic Lamp Reflector Project: Figure 12-5g, left, shows in perspective a paraboloid

Chapter 12, Problem 22

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Parabolic Lamp Reflector Project: Figure 12-5g, left, shows in perspective a paraboloid that forms the reflector for a table lamp. The reflector is 12 in. long in the x-direction and has a radius of 5 in. The circular lip with 5-in. radius is shown in perspective as an ellipse with major radius 5 in. and minor radius 2 in. Figure 12-5g a. Write parametric equations for the parabola shown. Pick a suitable t-range and plot the graph. Does the parabola start and end at the points shown in the figure? b. Write parametric equations for the ellipse. Plot the ellipse on the same screen as the parabola. If your grapher does not allow you to pick different t-ranges for the two curves, you will have to be clever about setting the period for the cosine and sine in the parametric equations so that the entire ellipse will be plotted. c. The figure on the right in Figure 12-5g shows the same lamp reflector rotated and translated so that its axis is at 40 to the x-axis. Find parametric equations of the rotated parabola and rotated ellipse. Plot the two graphs on the same screen. If the result does not look like the given figure, keep working on your equations until the figure is correct.