Please revise Completing the Square first...

Our aim is to get the equation into the form: (xh)2 + (yk)2 = r2

We complete the square on the x-related portion and on the y-related portion, at the same time.

`x^2+y^2+8x+6y=0`

Group the x parts together and the y parts togther:

`(x^2+8x)+(y^2+6y)=0`

Complete the square on each of the x and y parts.

`(x^2+8x+16)+(y^2+6y+9)` `=16+9` `=25`

`(x+4)^2+(y+3)^2=5^2`

This is now in the format we require and we can determine the center and radius of the circle.

So the centre of the circle is (-4, -3) and the radius is 5 units.

Circle radius 5

Note that the circle passes through (0, 0). This is logical, since (-4)2 + (-3)2 = (5)2

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