Question 313004
Start by setting this up to complete the square on the x and y terms.

x^2 + 6x +_____ +y^2 -2y+_____= 90 + _____ + _____


In order to complete the square, take HALF of the x and y coefficients, and SQUARE.  Add this number to each side of the equation.

x^2 + 6x +9 + y^2 - 2y+ 1 = 90 +9  +1
(x+3)^2 +(y-1)^2 = 100


This is the equation of a circle, whose center is at (-3,1).  The radius is 10.


Domain:  x extends from -3, a distance of 10 in each direction.  This would be from -3-10=-13 to -3 +10=7, including the endpoints.  Domain is [-13,7].


Range:  y extends from 1, a distance UP or DOWN 10 units.  This is from 1-10 =-9 to 1+10=11, including the endpoints.  Range is [-9,11].


Dr. Robert J. Rapalje, Retired