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Okay this is a second tutorial on circles for section 5.1 we were working on already looking at two examples of IPP in working with circles in standard form and finding the Centers and radii of these circles the third type of example is given a general form of a circle can we find the radius and in the center well in this form it's its difficult to tell what the radius might be and what the center point is going to be so what we have to do is we have to organize it and change it into its standard form, so I'm going to put this on a fresh piece because this is a longer type question, so the question was again 2y squared plus 2x squared minus 12x plus 8y minus 12 equals zero okay, so we want to take this down, and we want to make it into its standard form so what we're going to have to do is we're going to have to complete the square for the X points and the Y foot, so we're going to group the x squared and the X together first so that'd be 2x squared minus 12x here we're going to group the Y's then next remember these have to be the same to be a circle the coefficient in front of the Y squared and the coefficient in front of the x squared, so this is plus 2y squared plus 8x or pardon me Y, and then I'm going to bring the 12 to the other side so that negative 12 will become positive 12 over here, so we add 12 to both sides and that's what we're doing first then what we do is we have in order to complete the square we have to take out and divide everything by the number that's in front of the X and y squared, so we're going to divide everything by 2 so dividing by 2 we've got x squared minus 6x then we have y squared plus y squared pardon me plus 4y and then of course 12 divided by 2 is just 6 ok, so now we have it in sense that we don't have a large coefficient from the XY squared number values, and we can complete the square for each of these parts here now remember when you're completing the square you're going to be adding numbers in, so you have to be careful that you make sure you keep equating the numbers and keeping it equal on both sides of the equation ok, so that's what we'll do next so in order to complete the square you take half of the number that's what the non-squared term and square it and that's what you add in so x squared half of negative 6 is negative 3 negative 3 times negative 3 is 9, so this is negative 6x plus 9 plus y squared ok half of 4 is positive 4 is 2 2 squared is 4, so it's plus 4y plus 4 ok we added on both sides there we added a 9 and a 4 on the left side, so we need to add the 9 and 4 on this side otherwise we're changing the equation you know earlier when we divided by the 2 we didn't change the equation at all because we divided both sides by 2 same things here we added the same value to both sides 9 camp; 4 being 13 to both sides, so now we change this into this two it's factored square, so we take this, and we go that's X minus 3 all squared and when we take this we go oh that's why plus 2 all squared, and...
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