COMPLETE ALL. THEY MUST HAVE STEP BY STEP WITH EXPLANATIONS.

ORIGINAL ANSWERS

I WILL GIVE GOOD OR BAD FEEDBACK BASED ON THE FINAL SCORE. SO PLEASE TUTORS DO YOUR BEST, I NEED EXPERTS ON CALCULUS HERE, TAKE YOUR TIME BUT DO IT EXCELLENT. THANK YOU

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 100. The comet follows a parabolic path with directrix x = 70 and vertex at (60, 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) A system of equations is made up of an ellipse and a hyperbola. Part A: Create the equation of an ellipse centered at the origin, with a vertical major axis of 12 units and a minor axis of 6 units. Show your work. (3 points) Part B: Create the equation of a hyperbola centered at the origin, with a horizontal transverse axis, vertex at (-5, 0), and asymptotes of y = 1-x. Show your work. (4 points) Part C: Determine the domain of each conic section and use it to explain why there is no solution to the system. (3 points) An architect has designed two tunnels. Tunnel A is modeled by x2 + y? + 20x - 69 = 0, and tunnel B is modeled by x2 - 40x + 16y + 160 = 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)