An orbit of a satellite around a planet is an ellipse, with the planet at one focus of this ellipse. The distance of the satellite from this Star varies from 300000km to 500000km attained when the satellite is at each of the two vertex.find the equation of this ellipse If it s is at the origin and the vertex around the x-axis.assume all units are in 100000km.
To find the equation of the ellipse, we first need to determine the values of `a` and `b`, which represent the semi-major axis and semi-minor axis of the ellipse, respectively.
Given that the distance of the satellite from the planet varies from 300000km to 500000km, we can determine that 2a = 500000 and 2b = 500000 - 300000 = 200000.
Thus, a = 250000 and b = 100000.
Therefore, the equation of the ellipse is:
(x^2 / 250000^2) + (y^2 / 100000^2) = 1
Simplifying further, we get:
x^2 / 62500^2 + y^2 / 10000^2 = 1
Therefore, the equation of the ellipse is:
x^2 / 3906250000 + y^2 / 100000000 = 1