Question 1115399
start with y^2 - 6x + 16y + 94 = (y+C)^2 -B(x+A)


the left side of your equation is y^2 - 6x + 16y + 94.


rearrange and group the y terms to get (y^2 + 16y) - 6x + 94.


(y^2 + 16y) is equal to (y + 8) ^ 2 - 64.


this is because (y + 8) ^ 2 is equal to y^2 + 16y + 64, and, if you subtract 64 from both sides of that equation, you get (y + 8) ^ 2 - 64 = y^2 + 16y.



your expression on the left side of the equation becomes (y + 8) ^ 2 - 64 - 6x + 94.


combine like terms to get (y + 8) ^ 2 - 6x + 30


group the x and constant terms together and factor out the 6 to get:



(y + 8) ^ 2 - 6 * (x - 5).


your expression on the right side of the original equation is (y + C) ^ 2 - B * (x + A).


your equation becomes (y + 8) ^ 2 - 6 ( (x - 5) = (y + C) ^ 2 - B * (x + A).
 

this results in:


C = 8
B = 6
A = -5


when you replace A, B, and C with their respective values, the right side of your equation becomes (y + 8) ^ 2 - 6 * (x - 5), which is identical to the expression on the left side of your equation.


that means you're done.


the method you used was the completing the square method.


a reference on that method can be found at <a href = "http://www.purplemath.com/modules/solvquad3.htm" target = "_blank">http://www.purplemath.com/modules/solvquad3.htm</a>


any questions, give me a shout.