Question 629704
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Apparently you didn't complete the square correctly:

{{{x^2-y^2+2x+6y-9=0}}}

{{{x^2+2x-y^2+6y=9}}}

{{{(x^2+2x)-(y^2-6y)=9}}}

Half of 2 is 1.  Squared is 1

Add +1 inside the first parentheses and to the right side.

Half of -6 is -3.  Squared is 9.

Add +9 inside the second parentheses and since the second
parentheses is preceded by a - sign we add -9 to the right
side:

{{{(x^2+2x+1)-(y^2-6y+9)=9+1-9}}}

{{{(x+1)^2-(y-3)^2=1}}}

That's equivalent to

{{{(x+1)^2/1^2-(y-3)^2/1^2=1}}}

I think you can go from there.  If not post again.

Edwin</pre>