Answer:
Explanation:
To design a model of a solar system with a planet and a comet, we need to consider their orbits and their relative positions in space. Here are some steps to create the model:
Draw the planet's orbit: Since the planet's orbit is circular and centered at the origin with a diameter of 120, we can draw a circle with radius 60 and center at (0,0).
Draw the comet's path: The comet follows a parabolic path with directrix x = 85 and vertex at (75, 0). We can draw the directrix as a vertical line at x = 85 and draw the vertex at (75,0). Then, we can sketch the parabola using the vertex and directrix as guides. The axis of symmetry of the parabola is parallel to the directrix, so we can draw a horizontal line through the vertex to find the axis of symmetry. The focus of the parabola is located at (75, 30), which is the same distance from the vertex as the directrix.
Place the planet in its orbit: Since the planet's orbit is circular and centered at the origin, we can place the planet at any point on the circle. For example, we can place it at (60,0) or (-60,0) to create a more interesting dynamic with the comet's path.
Place the comet in its path: The comet will follow its parabolic path and pass by the planet at some point. We can choose a point on the parabola that intersects with the planet's orbit, such as (100,40), and place the comet there.
Add details: To make the model more realistic and visually appealing, we can add details such as stars, moons, and asteroids. We can also add labels and descriptions for the planet and comet.
Overall, the model should show the circular orbit of the planet and the parabolic path of the comet, with their relative positions in space. The model can be created using various materials such as paper, cardboard, or 3D printing.