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

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

mertsj · Answer

c^2=a^2-b^2
c^2=25-16
c^2=9
c=3, -3 so sun is at one focal point, let's say (3,0).  The center of the ellipse is (0,0) so from (0,0) to (3,0), is 300 million miles.