Question 216624
9x^2 -18x  +  16y^2 +64y = 71
.
9(x^2 -2x ) + 16(y^2 +4y ) = 71,,,complete  the  squares  remembering  the  last  term  = (2nd  term / 2) squared,,,,,and  add  compensating  amt  to  opposite  side  of  eqn
.
9(x^2 -2x +1) +16(y^2 +4y+4) = 71 +(9*1) + (16*4) = 144
.
9(x-1)^2 +16(y+2)^2 =144,,,,   divide  by  144
.
(1/16){(x-1)^2}  + (1/9){(y+2)^2} = 1
.
{(x-1)^2} / 16 + {(y+2)^2} / 9 =1,,,,,,,which  is  eqn  for  ellipse
.
Center  is  at  (1,-2),,,,,,,which  is  answer  (b)
.