If you want a proof you can do yourself, think of it like this.
Pick a value for r, say 10. That means r2 is 100.
So we want values of x and y where x2 + y2 = 100.
Pick a value for x. Let's go with 10. 102 is 100, so our equation looks like this: 100 + y2 = 100.
Re-arrange: y2 = 100 - 100 = 0. So y = sqrt(0).
Now divide x by 2. 52 = 25, so our equation looks like this: 25 + y2 = 100.
Re-arrange: y2 = 100 - 25 = 75. So y = sqrt(75).
Keep dividing x by 2, and rearrange the equation, and you'll keep getting points for y. Plus, you can't ever reach 0 by dividing by 2, so no matter how small you make the value of x, you'll always be able to get a value for y.
Pick a value for r, say 10. That means r2 is 100.
So we want values of x and y where x2 + y2 = 100.
Pick a value for x. Let's go with 10. 102 is 100, so our equation looks like this: 100 + y2 = 100.
Re-arrange: y2 = 100 - 100 = 0. So y = sqrt(0).
Now divide x by 2. 52 = 25, so our equation looks like this: 25 + y2 = 100.
Re-arrange: y2 = 100 - 25 = 75. So y = sqrt(75).
Keep dividing x by 2, and rearrange the equation, and you'll keep getting points for y. Plus, you can't ever reach 0 by dividing by 2, so no matter how small you make the value of x, you'll always be able to get a value for y.
