00:01
We need to complete the square in order to write the equation of the circle in standard form, identify the center and the radius, or explain why this can't be the equation of a circle.
00:11
So we're first going to move our 2x squared minus 36, leave some space, and then we have minus 2y squared, leave some space, equals move the 112 over 112.
00:28
We then pull out a common negative 2 from our first two terms.
00:31
So we have x squared plus 18 x and then we have minus 2 in parentheses y squared we have equals 112 so we take the middle term which is 18 divided by 2 and squares that's we're adding 81 which is really 81 times 2 well times negative 2 so 81 times negative 2 is negative 162 so we're adding a negative 162 so we're adding a negative to both sides.
01:09
So this becomes negative 2 times the quantity x plus 9 squared minus 2 times y squared is equal to 112 plus negative 162.
01:25
This is negative 50.
01:28
So then we divide everything by negative 2.
01:35
And we get the quantity x plus 9 squared plus y squared is equal to 25...