Question

Answer the following question.
Two satellites are orbiting Earth. The path of one satellite has the
equation x2 + y2 = 56 250 000. The orbit of the other satellite is
200 km farther from the centre of Earth. In one orbit, how much
Earther does the second satellite travel than the first satellite?​

Answer 1

Question:

Answer the following question.

Two satellites are orbiting Earth. The path of one satellite has the

equation x2 + y2 = 56 250 000. The orbit of the other satellite is

200 km farther from the centre of Earth. In one orbit, how much

Earther does the second satellite travel than the first satellite?

Step-by-step explanation:

The equation of the satellite's orbit is given in the form:

x2 + y2 = r2

Which is the equation of a circle, where r is the radius. Since the equation is:

x2 +y2 = 2250000

r2 is therefore 2250000, so take the square root of it to find r

r2 = 2250000

r = √2250000 = 1500km

As Robert showed, you don't actually need to find the radius in this case, but you can use it if you like. Since the second satellite's radius is given by (r+200)km, to find how much further the second satellite travels, subtract the circumference of the first satellite from the circumference of the second:

2π(r+200) - 2πr = 2π(r+200-r) [I took out a common factor of 2π from both terms]

= 2π*200 = 400π km

If you did this using the radii, you'd do it like so:

2π*1700 - 2π*1500 = 2π(1700-1500) [again, I took out a common factor of 2π]

= 2π*200 = 400π km

So, you can see we get the same answer regardless of whether we actually use 1700km and 1500km, or (r+200) and r as the radii.