Answer:
-3/4
Step-by-step explanation:
x^2+y^2=(x+2y)^2
x^2+y^2=(x+2y) (x+2y)
Foil the right side
x^2 +y^2 = x^2 + 2xy + 2xy + 4y^2
Combine like terms
x^2 +y^2 = x^2 +4xy + 4y^2
Subtract x^2 +y^2 from each side
x^2 +y^2 - x^2 - y^2 = x^2 +4xy + 4y^2- x^2 - y^2
0 = 4xy + 3y^2
Subtract 3y^2 to each side
-3y^2 = 4xy
Divide each side by y^2
-3y^2 / y^2 = 4xy/ y^2
-3 = 4x/y
Divide each side by 4
-3/4 = x/y
The ratio is -3/4
