How do I solve the following word problem : A satellite orbits Earth in a circular path with equation x squared + y squared = 1.44 times 10 to the power of 8. With distances measured in kilometers. Another satellite orbiting in the same plane passes through the point (8000,9800). Is this satellite inside the orbit of the first one? Thank you.

Question

---> Here's what I thought of this question.

1.I should use an equation, so perhaps r^2=(x)^2 + (y)^2.
2.I have to figure out what the radius is though, but I don't know what 10 the power of 8 is, once I do, that will be multiplied by 1.44, and that will be the radius of circle, therefore, any other point from the point of origin to the end point of the circle will be equivalent to what the answer of the first equation is.
As long as I can figure out what 10 to the power of 8 is, I can do the rest on my own. Considering that we are starting from the point of origin, (0,0) it will be 8000^2+9800^2=r^2 Thanks!

Answer 1

For the second part i got r=12650.69, am I correct?

Answer 2

the equation of a circle is
x^2 + y^2 = r^2 ---> radius is r

yours:
x^2 + y^2 = 1.44(10^8), so the radius is 1.2(10^4)

you are correct to find
8000^2 + 98000^2 = r^2
r^2 = 9668000000
= 9.668(10^9) , which is clearly > 1.44(10^8)

So the point lies outside the circle of the first satellite.

10^2 = 100
10^3 = 1000
10^4 = 10000 , can you see the pattern?
..
10^8 = 100,000,000
10^9 = 1,000,000,000 , clear bigger than 10^8 by a factor of 10