please help me answer this topic is "Solving Problems Involving Iconic Functions"

Learning Task 5: Solve each situational problem involving conic sections. 1. A mathematician was shopping for furniture when he stumbles across the clocks area and finds different sizes of clocks. He then thinks what he's finding in the clock that he would buy. He tells the shopkeeper that he would like a clock with a diameter that is irra- tional. The shopkeeper then gave him 3 clocks as a challenge. The first clock had this equation: x3 + y# - 32x + 18x + 193 = 0 ; the second had the ends of its diameter on the points (3,6) and (9,8); the last clock had an area of 144 square units. Which clock(s) would fit the mathematician's request? 2. An engineer is working on making a diagram for the cooling tower he was going to con- struct in the future. Cooling towers can be seen as towers with inward-curving sides, or simply, hyperbola-looking sides. His daughter asks him how high the center of the hyper- bolic sides of the tower was y = _- x + 15 , and he answers that the center can be situat ed at (0, 15) in the Cartesian plane. The engineer then says that the asymptotes of the hy- perbola are the following: , and the area of its auxiliary rectangle is 168 square units. The daughter then finds the foci of the hyperbola. At what points on the Cartesian plane are these foci found on? C 3. Suspension bridges are known to be normal around the world, especially in developed countries. These bridges usually have towers of some sort and cables, both of which have great importance in the integral stability of the bridge. A STEM Student makes some plans for his project on a suspension bridge model. He first tries to draw his model. The two tow- ers are 12 meters high and 20 meters apart (10 meters away each from the origin in the center), and the cable he drew between and from the top of the two towers are of course, parabolic. The lowest point of the cable is 3 meters above the origin. He shows this model to his teacher, and the teacher asks him, "What is the vertical distance from the road to the cable at 5 meters away from the center?" What is the answer to the teacher's question? 4. A certain celestial body is orbiting around a star somewhere in space. An astronomer tries to graph out the elliptical orbit of the celestial body using dimensional analysis and scaling. In his drawing, the celestial body is in the origin, and he finds out that the equa- tion of the elliptical orbit is 4x3+ 9y' -256x + 342y + k= 0 for some value of k. If his findings are true, find the location of the star (the center of the ellipse) in the Cartesian plane