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. Write the equation for Tunnel A in standard form and determine the conic section. Show your work. Write the equation for Tunnel B in standard form and determine the conic section. Show your work. 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.
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