Earth orbits the sun in an elliptical pattern. the equation of earths path is (x+2.5)/22350.25 + y^2/22344=1 where the measurements represent millions of kilometers. The sun is located at the focus (0,0). In january, earth id located at one vertices which is 147 million kilometers from the sun. Determine earths distance from the sun in july.

Correct answer is 152 million kilometers but i am not sure how? Help anyone?

1 answer

First of all, if it is an ellipse then you have a typo, try ...

(x+2.5)^2/22350.25 + y^2/22344=1
or
(x+2.5)^2/149.5^2 + y^2/149.479^2 = 1

x^2/149.5^2 + Y^2/149.479^2 has been moved 2.5 units to the left.

The farthest point (Jan) is 149.5 - 2.5 million of km away, which was the given.

Assuming that July corresponds with the vertical vertex,
d^2 = 149.479^2 + 2.5^2
d = appr 149.5

in order for 152 to be the correct answer, we would need a vertical shift of 2.5 as well. 149.5+2.5 = 152
But your equation does not show that