If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the o

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?

If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?

Correct Answer: -2/3

Step 1: Identify the given equation, which is 3x^2 + 2xy - y^2 = 0.
Step 2: Recognize that this equation represents two lines that intersect at the origin (0,0).
Step 3: Identify the coefficients in the equation: a = 3 (coefficient of x^2), c = 2 (coefficient of xy).
Step 4: Use the formula for the product of the slopes of the lines, which is -c/a.
Step 5: Substitute the values into the formula: -c/a = -2/3.
Step 6: Calculate the result: The product of the slopes is -2/3.

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