Question 1082829
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Instead of doing yours for you, I will do another
one exactly like yours, which you can use as a model 
to do yours by:

{{{ x^2 + y^2 - 6x + 8y = 1}}}

Rearrange terms so that x terms are together and 
y terms are together.

{{{ x^2 - 6x + y^2 + 8y = 1}}} 

We insert blanks where we must insert numbers
which complete the squares:

{{{ x^2 - 6x + "__"+y^2 + 8y +"__"= 1+"__"+"__"}}}

We complete the square to find what goes in the first 
blanks on each side of the equation.

1. Multiply the coefficient of x by 1/2.
    (-6)(1/2) = -3
2. Square -3, get (-3)² = +9
3. Add to both sides in the first blanks on each
   side.

{{{ x^2 - 6x + 9 +y^2 + 8y +"__"= 1+9+"__"}}}

We also complete the square to find what goes in the 
remaining blanks on each side of the equation.

1. Multiply the coefficient of y by 1/2.
    (+8)(1/2) = +4
2. Square +4, get (+4)² = +16
3. Add to both sides in the remaining blanks on each
   side.

{{{ x^2 - 6x + 9 +y^2 + 4y + 16 = 1+9+16}}}

Next we factorise the first three terms on the left
as (x-3)² and the last three terms on the left as (y+4)²
and combine terms on the right as 26

{{{(x-3)^2+(y+4)^2=26}}}

We compare that to the standard equation for a circle:

{{{(x-h)^2+(y-k)^2=r^2}}}
                      __
and h=3, k=-4, and r=&#8730;26
                                   __
So centre is (3,-4), radius = r = &#8730;26 

Now you can do yours exactly the same way.

Edwin</pre></b>