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.

Part B: Write the equation of the comet's path in standard form. Show your work.

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.