00:01
In this question, we want to find the center and radius of the circle with the given equation.
00:05
Here i have 4x squared plus 16x plus 15 plus 4y squared plus 6y, and i'm setting all of this equal to zero.
00:23
So the first thing i'm going to do is subtract the 15 to the right -hand side so that i have 4x squared plus 16x plus 4y squared plus 6y equals negative 15.
00:42
Now my eventual trick is going to be to complete the square.
00:46
So because of that, i want coefficients of 1 on both x squared and y squared.
00:53
That's going to require that i divide both sides by 4.
00:57
So if i divide through by 4, what do we get? we get x squared plus 4x plus y squared plus 6 over 4, which is 3 over 2, times y equals negative 15 quarters.
01:19
I'm going to go to this x quadratic.
01:21
To complete the square, i take half of my b term.
01:25
Half of 4 is 2.
01:27
Square it so that i have x squared plus 4x plus 4.
01:35
With my second quadratic, i again take half of my b term.
01:42
Half of 3 halves is 3 quarters.
01:46
Square that 9 sixteenths.
01:49
So i'm going to add 9 sixteenths...