Question

Nabil is writing a science fiction novel that takes place in another galaxy. In her galaxy, all the planets travel in an elliptical orbit around their star. The majority of the plot of Nabil’s story takes place on the planet Tanus which orbits a star named Ini. The length of Tanus’ major axis is 150 million miles and the length of its minor axis is 75 million miles. The star Ini is located at a focus of the elliptical orbit.

Suppose that Nabil would like to create a model that shows the path of Tanus’ orbit around Ini. For ease of programming, Nabil would like Ini to be located at the coordinates (0, 0). Write an equation that models the movement of Tanus around Ini, where Ini is located at (0, 0). Explain the changes to your equation.

1. Giakhanh
The equation that models the movement of Tanus around Ini, where Ini is located at (0, 0) is x^2/75^2 + y^2/37.5^2 = 1

### Write an equation that models the movement of Tanus around Ini, where Ini is located at (0, 0)

The given parameters are:
The length of Tanus’ major axis = 150 million miles
The length of its minor axis = 75 million miles
The center of the ellipse = (0, 0) — the location of Ini
When the coordinate of the center of an ellipse is (0, 0), the standard form of the ellipse is represented as:
x^2/a^2 + y^2/b^2 = 1
Where:
Length of the major axis = 2a
Length of the minor axis = 2b
This means that:
2a = 150 and 2b = 75
Divide both sides of 2a = 150 by 2
a = 75
Divide both sides of 2b = 75 by 2
b = 37.5
Substitute b = 37.5 and a = 75 in the standard form of the ellipse represented as: x^2/a^2 + y^2/b^2 = 1
x^2/75^2 + y^2/37.5^2 = 1
Hence, the equation that models the movement of Tanus around Ini, where Ini is located at (0, 0) is x^2/75^2 + y^2/37.5^2 = 1