The correct option is C x+2y+4=0
x2+4xy+4y2+3x+6y−4=0
Writing equation in terms of y, we get
4y2+(4x+6)y+(x2+3x−4)=0
Now, using quadratic formula, we have
y=−(4x+6)±√(4x+6)2−4⋅4⋅(x2+3x−4)2⋅4
⇒y=−(4x+6)±102⋅4
⇒y=−(2x+3)±54⇒y=−x+12 or y=−x−42⇒x+2y−1=0 or x+2y+4=0
Alternate Solution:
x2+4xy+4y2+3x+6y−4=0⇒(x2+4xy+4y2)+(3x+6y)−4=0⇒(x+2y)2+3(x+2y)−4=0⇒((x+2y)+4)((x+2y)−1)=0⇒x+2y+4=0 or x+2y−1=0