Area of the triangle formed by the lines y2−9xy+18x2=0 and y=6 is_______

we have y2−9xy−18x2=0 or y2−6xy−3xy+18x2=0or y(y−6x)−3x(y−6x)=0or y−3x=0 and y−6x=0 The third line is y=6. Therefore, the area of the triangle formed by these lines=12|012      066       111|=12|6−12|=3 units2