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

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

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

$\frac{x^2}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1$

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

Thus, option C is correct.