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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.

The Equation That Models Earths Elliptical Orbit Around The Sun Is X2522235025y2223441 In Millions Of Kilometers If The Sun Is Located At One Focus And Its Coor class=

Sagot :

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

[tex]\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}[/tex]

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

[tex]\frac{x^2}{(149.5)^2}+\frac{y^2}{(149.479)^2}=1[/tex]

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

Thus, option C is correct.

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