If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 intersect at the origin, what is the product of their slopes?

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Q: If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 intersect at the origin, what is the product of their slopes?

Solution: The product of the slopes of the lines represented by ax^2 + bxy + cy^2 = 0 is given by c/a. Here, c = 2 and a = 3, so the product is 2/3.

Steps: 7

Step 1: Identify the equation given, which is 3x^2 + 4xy + 2y^2 = 0.
Step 2: Recognize that this equation represents two lines that intersect at the origin.
Step 3: Understand that the general form of a conic section can be expressed as ax^2 + bxy + cy^2 = 0.
Step 4: Identify the coefficients from the equation: a = 3, b = 4, and c = 2.
Step 5: Use the formula for the product of the slopes of the lines, which is c/a.
Step 6: Substitute the values of c and a into the formula: c = 2 and a = 3.
Step 7: Calculate the product of the slopes: 2/3.

If the lines represented by the equation 3x^2 + 4xy + 2y^2 = 0 intersect at the origin, what is the product of their slopes?

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