The lines represented by the equation 6x^2 - 5xy + y^2 = 0 are:
Correct Answer: The lines are perpendicular.
- Step 1: Start with the equation 6x^2 - 5xy + y^2 = 0.
- Step 2: Recognize that this is a quadratic equation in terms of x and y.
- Step 3: Rewrite the equation in the standard form of a conic section, which can represent two lines.
- Step 4: Use the quadratic formula or factorization to find the slopes of the lines.
- Step 5: Calculate the slopes (m1 and m2) of the two lines obtained from the equation.
- Step 6: Check if the product of the slopes (m1 * m2) equals -1.
- Step 7: If the product is -1, then the lines are perpendicular.
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