1. ## Writing Equations

Write a single equation that describes the set of all points (x, y) that are 5 units from the origin or less that 10 units from the point (10, 0).

2. ## Re: Writing Equations

Originally Posted by thamathkid1729
Write a single equation that describes the set of all points (x, y) that are 5 units from the origin or less that 10 units from the point (10, 0).
For starters...

The set of points that are 5 units from the origin would be the circle of radius 5 centred at the origin. What would the equation of the circle be?

The set of points that are less than 10 units from the point (10, 0) would be the region inside (but not including) the circle of radius 10 centred at (10, 0). What would the inequation of that region be?

3. ## Re: Writing Equations

So, x^2 + y^2 = 25 and (x-10)^2 + y^2 < 100. But how would I write this as one equation???

4. ## Re: Writing Equations

Originally Posted by thamathkid1729
So, x^2 + y^2 = 25 and (x-10)^2 + y^2 < 100. But how would I write this as one equation???
\displaystyle \displaystyle \begin{align*} \left\{(x, y) | x^2 + y^2 = 25 \cup (x - 10)^2 + y^2 < 100\right\} \end{align*}

5. ## Re: Writing Equations

$\displaystyle \{(x,y) | x^2+y^2=25 \, ; \, \frac{5}{4} < x \le 5\}$

6. ## Re: Writing Equations

Originally Posted by skeeter
$\displaystyle \{(x,y) | x^2+y^2=25 \, ; \, \frac{5}{4} < x \le 5\}$
The wording of the question implies that you can accept any point that is on EITHER region (i.e. the union) instead of only accepting the points that are on BOTH regions (i.e. the intersection).

The OP needs to clarify this...

7. ## Re: Writing Equations

Originally Posted by Prove It
The wording of the question implies that you can accept any point that is on EITHER region (i.e. the union) instead of only accepting the points that are on BOTH regions (i.e. the intersection).

The OP needs to clarify this...
true ... I wrote it as the intersection, the set of all points 5 units from the origin and less than 10 units from (10,0).

Oh well, both possibilities are covered.

8. ## Re: Writing Equations

I was looking for the union