Question

The Earth’s path around the Sun is elliptical, and the Sun is situated at one of the foci. If the Earth’s orbit can be represented by x2/25 + y2/16 = 1, where x and y are measured in 100 million miles, what is the distance from the center of Earth’s elliptical path to the sun?
A. 100 million miles
B. 200 million miles
C. 300 million miles
D. 400 million miles

Answer 1

What does it mean by "center of Earth's elliptical path?"
One of the vertices?

Answer 2

or do you mean what is the average distance ?

Answer 3

Well, the astronomical fact is that the average distance from Earth to Sun is between 90 and 100 million miles, but that might not necessarily be relevant in an example math problem..

Answer 4

^2 = b^2 + c^2
25 = 16 + c^2
c = 3
Plot it as (0, 3). The major axis is 2a.
Therefore, the distance between the center and the sun or focus, is 3,000,000.

Answer 5

I think they're talking about from the center of the orbit to the edge of the elliptical.

Answer 6

Wait, it would be (3, 0)

Answer 7

The distance is 3,000,000.

Answer 8

@MindAuthentic It means the center of the ellipse to the sun which is at one of the focii.

Answer 9

@Calcmathlete , 3 million is not an answer choice. Check your units.

Answer 10

300,000,000

Answer 11

I read it as each unit is 1,000,000 not 100,000,000.

Answer 12

Thanks Everyone For The Help

Answer 13

You're welcome :)

Answer 14

Would've been cool if they used the actual astronomical data to get the ellipse equation..
The major axis of Earth's orbit is 186 million miles, with distance from Sun(focus) to nearest vertex = 91 million miles. Anyone care to find the correct equation given that data? ;-)