Find the area of the region enclosed by the graph of the equation

This is the equation of a circle...put it into standard form to find the radius....then area = pi r^2

x^2 - 8x        + y^2-9y        =   - 105      ' complete the square' for x and y

(x-4)^2          +  (y-4.5)^2  =  - 105  +16 + 20.25            ( are you SURE that was a  - 105 ??)

                                        I will assume -105 is supposed to be  - 10.5

                                          - 10.5 + 16 + 20.25 = r^2    r = 5.074 units

Then   pi r^2 =   25.75 pi units²