Conic section

I didn't know how to this conic problems and I need help

2. (10 points) One of the largest domes in the world belongs to St. Paul's cathedral in London with a diameter of 34 meters. Christopher Wren was the architect and enlisted Robert Hooke to design the largest dome possible that would not need any support. Hooke figured out that if you were to hold a chain by its ends, the U-shaped result would be the shape which minimizes the energy of the chain. This U shape is a catenary. He realized that to create a dome where the weight is spread out as much as possible, you would "flip" the chain upside down. This would let them build the largest dome possible (which could support its own weight). (2.1) In this problem we will model this as a (2.2) Sketch this model of dome, label the ver- parabola. Assume the top of the dome tex, focus, and draw the directrix. Show is the vertex and has coordinates at (0, 0) 3 key points the graph goes through and and that the diameter of the dome is the label them with their coordinates. length of the latus rectum (the focal diam- eter). Using this information, determine the equation of St. Paul's Cathedral's dome. -20 -15 -10 -5 5 10 1 20 Work: (2.3) Although we can model the cathedral dome with a parabola, the actual shape of this dome is more closely modeled by d(x) = - 491325. Using a graph- ing tool (for example Desmos), graph your parabola and d. In the box be- low, describe the difference between the two graphs. If d is the optimal roof de- sign, make a prediction on how well the parabola dome might be able to support its own weight. Answer: Answer: St. Paul's dome isn't actually a parabola, it's a catenary, which seems to resemble to a parabola. You can read more about catenaries here: https:/ /en. wikipedia.org/wiki/Catenary