The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to b

The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:

The condition for the lines represented by the equation x^2 + y^2 + 2xy = 0 to be coincident is:

Step 1: Start with the given equation: x^2 + y^2 + 2xy = 0.
Step 2: Recognize that this equation can be rearranged into a standard quadratic form in terms of y: y^2 + 2xy + x^2 = 0.
Step 3: Identify the coefficients of the quadratic equation: a = 1 (coefficient of y^2), b = 2x (coefficient of y), c = x^2 (constant term).
Step 4: Recall the formula for the discriminant of a quadratic equation, which is D = b^2 - 4ac.
Step 5: Substitute the coefficients into the discriminant formula: D = (2x)^2 - 4(1)(x^2).
Step 6: Simplify the discriminant: D = 4x^2 - 4x^2 = 0.
Step 7: Conclude that for the lines to be coincident, the discriminant must equal zero, which we have shown is true.

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