Today we're going to look at equations whose graphs give us circles. These equations will be a bit different from the ones we've seen before. However, it's good for us to examine different types of equations to see what their graphs will look like. In the video below, we'll give the mathematical definition of a circle, determine what sorts of equations have graphs in the shapes of circles, and then go through some example problems where we sketch a couple of graphs.
Make sure to look at all of the example problems at the link below, as each one covers a slightly different situation.
I want to do a very quick review about a process called completing the square, which we'll need for the last part of today's lesson. We'll use completing the square to take a polynomial that's not a perfect square and then turn it into one.
Check out some of these example problems for more practice:
In this next section, we're going to see some examples that aren't in the form (x - h)^2 + (y - k)^2 = r^2. To take these examples and put them into standard form for a circle, we'll need to use the completing the square method.
I have recorded several videos of worked-out example problems, which you can access at the link below. Once you start to get the hang of the problems, try them out before you watch the video to see if you're solving them correctly. And if you're not, compare your steps to those in the video to learn from your mistakes. This is a great opportunity for you to make sure you're doing each step correctly and mastering these skills!
Finally, remember to complete the homework assignment titled "Circles" which is available on WebAssign.