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 120. The comet follows a parabolic path with directrix x = 85 and vertex at (75, 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
path of the comet. Show your work and round answers to the hundredths place.