An orbit of a satellite around a planet is an ellipse with the planet at one focus of this ellipse. The distance of the sateihte from this stor varies froth 300,000 km to 500.000 km attained when the satellite is at each of the two vertices Find the equation of this ellipse if its center is at the origin and the vertices are on the r-axis. Assume all units are in 100.000 km

Given that the orbit of the satellite is an ellipse with the planet at one focus and the vertices on the r-axis, we can find the equation of the ellipse.

### Step 1: Understand the ellipse parameters
- The center of the ellipse is at the origin \((0, 0)\).
- The vertices of the ellipse are on the r-axis (which we'll consider as the x-axis).

Given:
- The distance from the satellite to the planet varies from 300,000 km to 500,000 km.
- The distance is measured along the major axis, from the center of the ellipse to the vertices.

### Step 2: Assign the values to the ellipse parameters
Since the units are in \(100,000 \text{ km}\), let's express the distances as:
- Minimum distance (closest to the planet): \(3\) units (\(300,000\) km).
- Maximum distance (farthest from the planet): \(5\) units (\(500,000\) km).

These distances correspond

Learn how to find the equation of an ellipse describing the orbit of a satellite around a planet, with the planet at one focus and vertices on the r-axis. Detailed step-by-step solution included, covering conic sections and ellipse geometry concepts.

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