Now that the satellite has been launched (i.e. Ch. 12 Lab),Earth is hopeful to get a more reliable eye on space anomalies.Shortly after the satellite's course around Jupiter, communicationstarted to get more and more sporadic and weaker in signal. Tocounter this, a new satellite dish will be designed, specificallytargeting the new satellite. Satellite dishes follow the shape of aparaboloid. The equation of a paraboloid is as follows:z=x^2/a^2+y^2/b^2 Where a and b could be the same number (dependingon the desired shape). When you are designing this dish, whereshould you place the receiver? The receiver is like the ‘antenna’,receiving the data signals. Could the effectiveness of the receiverbe changed if the ratio a/b is changed? A preliminary design isstarted with the dish’s circular radius of 20 feet, and a depth of5 feet. What is the equation for this paraboloid? Hint: a = b, forthis design. When the dish is a circular paraboloid (again a = b),a two-dimensional model could be viewed with the equation: x^2=4py, where p is the distance from the parabola's vertex to its focus.This equation can be revolved around the y-axis to form the shapeof the satellite dish. Using the dimensions of the dish in #2, findthe equation of the parabola in two-dimensions. Where should thereceiver be placed? If the graph is revolved around the y-axis,what is the surface area of the satellite dish? From #3, find thecost of the dish itself when the material to make the dish costs$1,500 per square foot (it is a high quality satellite dish!). Manysatellite dishes today are elliptic paraboloids (now a ≠ b), forreasons of reducing interference. But, would this change of shapealso change where to place the receiver? Let’s use a satellite dishwhich has a 20-foot radius in the x-direction, and has a 10-footradius in the y-direction. If a single receiver is placed at 10feet from the vertex, what must the depth be in the x-direction andy-direction, separately, in order that the signal is maximized?What would a function look like for the depth of the dish at anyparticular place on the rim? Is there any theoretical reason to usean elliptic paraboloid vs. a circular paraboloid? Explain yourreasoning. Thank you.