An architect has designed two tunnels. Tunnel A is modeled by x + y + 28x + 52 = 0, and tunnel B is modeled by x - 36x + 16y + 68 = 0, where all measurements are in feet. The architect wants to verify whether a truck that is 8 feet wide and 13.5 feet high can pass through the tunnels. Part A: Write the equation for Tunnel A in standard form and determine the conic section. Show your work. (4 points) Part B: Write the equation for Tunnel B in standard form and determine the conic section. Show your work. (4 points) Part C: Determine the maximum height of each tunnel. Is the truck able to pass through either tunnel without damage? If so, which tunnel(s) and why? Show your work. 1. (03.02, 03.03 HC) Lyra is designing a model of a solar system with a planet and a comet. The planet has a circular orbit, centered at the origin with a diameter of 140. The comet follows a parabolic path with directrix x = 100 and vertex at (85, 0). Part A: Write the equation of the planet's orbit in standard form. Show your work. (2 points) Part B: Write the equation of the comet's path in standard form. Show your work. (4 points) Part C: Identify all points where the planet's orbit intersects the path of the comet. Show your work and round answers to the hundredths place. (4 points) 4. (03.07 HC) In a solar system, two comets pass near the sun, which is located at the origin. Comet E is modeled by (x-13) 144 25 1, where all measurements are in astronomical units. = (x+16) 400 + = 1 and Comet H is modeled by 144 Part A: What are the vertices for the path of Comet E? Show your work. (4 points) Part B: Which comet travels closer to the sun? Give evidence to support your answer. (5 points) Part C: What key feature does the sun represent for both comets? Give evidence to support your answer. (6 points)