 Let's look at finding the equation of a circle whose diameter has n points, negative 10, negative 8, and 8, negative 4. We want to write it in the form x minus h squared plus y minus k squared is equal to r squared, and then be able to find the center in radius. So to start, let's look at finding the center. What we can look at then, because we have the n points of the diameter, is finding the midpoint between those two points. And to find the x coordinate of our midpoint, we simply look at finding the average of our x values. So we have negative 10 plus 8 over 2 gives us negative 2 over 2, which is negative 1. To find the y coordinate, we'll take the average of our y values to negative 8 plus negative 4 over 2. We have negative 12 over 2, which is negative 6. And so the center of our circle is negative 1, negative 6. And we know in our form, x minus h squared plus y minus k squared equals r squared, that h represents the x coordinate of our center, and k represents the y coordinate of our center. And so we know that h equals negative 1, and k equals negative 6. We can substitute these into the formula. And so we have x minus negative 1 squared, or x plus 1 squared, and y minus negative 6 squared, or y plus 6 squared, equals r squared. Notice that we're still missing the last constant, r. And we can find that by substituting in one of our points in for x and y. We could use either point, I'm going to use the point negative 10, negative 8. And so we have negative 10 plus 1 squared plus negative 8 plus 6 squared equals r squared. And now we simplify it. So negative 10 plus 1 squared gives us negative 9 squared, and negative 8 plus 6 squared gives us negative 2 squared. Negative 9 squared is 81, negative 2 squared is 4. And so we have r squared equals 85. We know then that our radius is v squared of 85. And our circle is x plus 1 squared plus y plus 6 squared equals 85.