Question

The equation that models Earth's elliptical orbit around the sun is (x+2.5)^2/22,350.25+y^2/22,344=1 in millions of kilometers. If the sun is located at one focus and it’s coordinates are (0,0), find Earth's farthest distance from the sun in millions of kilometers.

Answer 1

Given the equation of the elliptical orbit is (x+2.5)^2/22,350.25+y^2/22,344=1.

This equation can be written as

`\begin{gathered} ((x+2.5)^2)/(22350.25)+(y^2)/(22344)=1 \\ ((x+2.5))/((149.5)^2)+(y^2)/((149.479)^2)=1 \end{gathered}`

Now, if we shift this path by 2.5 units to left then we get

`(x^2)/((149.5)^2)+(y^2)/((149.479)^2)=1`

The farthest distance of the earth from the sun will be 149.5 - 2.5 = 147 million of kilometers

Thus, option C is correct.