Question
An architect has designed two tunnels. Tunnel A is modeled by x 2 + y 2 + 30 x + 56 = 0, and tunnel
An architect has designed two tunnels. Tunnel A is modeled by x2 + y2 + 30x + 56 = 0, and tunnel B is modeled by x2 - 30x + 16y - 95 = 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. (7 points)
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