The lines represented by the equation 6x^2 - 5xy + y^2 = 0 are:

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Question: The lines represented by the equation 6x^2 - 5xy + y^2 = 0 are:

Options:

Correct Answer: Perpendicular

Solution:

The lines are perpendicular if the product of their slopes is -1, which can be verified from the equation.

The lines represented by the equation 6x^2 - 5xy + y^2 = 0 are:

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.

Quadratic Equations – Understanding how to factor or analyze quadratic equations to find lines represented by them.
Slope of Lines – Knowledge of how to determine the slopes of lines and the condition for perpendicularity.