Given equation, 9x2+4y2+10x+12y+1=0...(i) Let origin (0,0) shifted to (h,k), then x→x−h and y=y−k, putting in Eq. (i), we get 9(x−h)2+4(y−k)2+10(x−h)+12(y−k)+1=0 ⇒9x2+4y2+9h2+4k2−18xh−8yk+10x−10h+12y−12k+1=0 ⇒(9x2+4y2)−x(18h−10)−y(8k−12)+(9h2+4k2−10h−12k+1)=0 If equation is without x and y term, then 18h−10=0⇒h=