Now, equation 2x2+xy−6y2+k=0 Old equation 2x2+xy−6y2−13x+9y+15=0 Origin is shifted to (a,b) 2(x−a)2+(x−a)(y−b)−6(y−b)2−13(x−a)+9(y−b)+15=0 ∴ Coefficient of x=0 4a+b−13=0 Coefficient of y=0 a−12b+9=0 Solving Eqs. (i) and (ii) we get a=3 and b=1 ∴ Constant ⇒k=2a2+ab−6b2−13a+9b+15 Put a=3 and b=1 k=0
