find the the the the the centre of the hyperbola x^2+4y^2+xy+8x-2y+7=0 is

Method to find centre of any conic :- Partially differentiate wrt x and also wrt y.You will get 2 equations which are equations of two straight lines (These lines don`t represent anything, neither asymptotes or anything). On solving these 2 lines we get centre of conic (Valid for every 2nd degree conic).