# Thread: Weather Satellites

1. ## Weather Satellites

Earth is represented on a map of a portion of the solar system so that its surface is a circle with equation x^2 + y^2 + 2x + 4y - 4091 = 0. A weather satellite circles 0.6 unit above Earth with the center of its circular orbit at the center of Earth. Find the equation for the orbit of the satellite on this map.

Seeking the first-two steps.

2. ## Re: Weather Satellites

Put the given circle representing the surface of the Earth into the form:

$\displaystyle (x-h)^2+(y-k)^2=r^2$

Then the trajectory of the satellite will be:

$\displaystyle (x-h)^2+(y-k)^2=\left(r+\frac{3}{5}\right)^2$

3. ## Re: Weather Satellites Originally Posted by MarkFL Put the given circle representing the surface of the Earth into the form:

$\displaystyle (x-h)^2+(y-k)^2=r^2$

Then the trajectory of the satellite will be:

$\displaystyle (x-h)^2+(y-k)^2=\left(r+\frac{3}{5}\right)^2$
x^2 + 2x + y^2 + 4y - 4091 = 0

x^2 + 2x + y^2 + 2y = 4091

x^2 +2x + 1 + y^2 + 4y + 4 = 4091 + 1 + 4

(x + 1)^2 + (y + 2)^2 = 4096

(x + 1)^2 + (y + 2)^2 = 64

So, r = 64.

The equation I seek is

(x + 1)^2 + (y + 2)^2 = (64 + 3/5)

4. ## Re: Weather Satellites Originally Posted by harpazo x^2 + 2x + y^2 + 4y - 4091 = 0

x^2 + 2x + y^2 + 2y = 4091

x^2 +2x + 1 + y^2 + 4y + 4 = 4091 + 1 + 4

(x + 1)^2 + (y + 2)^2 = 4096

(x + 1)^2 + (y + 2)^2 = 64 …. this should be 64^2

So, r = 64.

The equation I seek is

(x + 1)^2 + (y + 2)^2 = (64 + 3/5)^2

Now evaluate the RHS.

5. ## Re: Weather Satellites Originally Posted by Debsta Now evaluate the RHS.
RHS = (323/5)^2

RHS = (104,329)/5

Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/5

6. ## Re: Weather Satellites Originally Posted by harpazo RHS = (323/5)^2

RHS = (104,329)/5

Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/5

RHS should be on 25 not 5.

7. ## Re: Weather Satellites Originally Posted by Debsta RHS should be on 25 not 5.
Yes, you are right. I forgot to square 5.

RHS = (323/5)^2

RHS = (104,329)/25

Final Answer: (x + 1)^2 + (y + 2)^2 = (104,329)/25

Correct?