00:02
Alright, here we have the equation of a circle and we want to find the center in radius and graph the circle and so we're going to use completing the square to help us transform this equation into standard form so i'm going to rewrite this as x squared minus 21 x and then i'll need to add a number to complete the square and then we have y squared minus 33 y and we're going to need to add a number to complete the square i'm going to subtract 17 from both sides and then whatever numbers are added to the left also need to be added to the right to keep the equation balanced.
00:35
So to figure out what to add, we take half of 21 and square it.
00:39
So half of 21 is 21 halves and we square that and we get 441 fourths.
00:46
And then we take half of 33, which is 33 halves and we square it and we get 1 ,089 fourths.
00:55
So we need to add those numbers to the other side of the equation as well.
01:02
Okay, so now we can factor the x -trimomial into x -minus 21 -halfs, quantity squared and we can factor the y trinomial into y minus 33 halves quantity squared and when we add all the numbers on the right side we end up with 1462 fourths okay so from this equation we can see that the center of the circle is going to be the point 21 halves 33 halves and for the sake of graphing it's more convenient to think of that as 10 and a half 16 and a half and then to get the radius we take the square root of 1462 fourths.
01:44
And so the numerator is square root 1462 and the denominator is 2.
01:48
And the approximate value is what we're going to need for graphing...
