I also need help with this homework please

Question

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.

Answer 1

Part A: x² + y² = 4900.

Part B: p = 85 - 100 = - 15; y² = - 60(x - 85)

Part C: x² - 60(x - 85) = 4900; x² - 60x + 200 = 0; x = 30 ± 10√7;

x = 30 + 10√7 = 56.46; y = ± 41.38; (56.46, 41.38) and (56.46, - 41.38)

x = 30 - 10√7 = 3.54; y = ± 69.91; (3.54, 69.91) and (3.54, - 69.91)