The pair of lines represented by the equation 2x^2 - 3xy + y^2 = 0 has slopes m1

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Question: The pair of lines represented by the equation 2x^2 - 3xy + y^2 = 0 has slopes m1 and m2. What is the product m1*m2?

Options:

Correct Answer: -2

Solution:

The product of the slopes of the lines is given by m1*m2 = c/a = 1/2 = -2.

The pair of lines represented by the equation 2x^2 - 3xy + y^2 = 0 has slopes m1 and m2. What is the product m1*m2?

The pair of lines represented by the equation 2x^2 - 3xy + y^2 = 0 has slopes m1 and m2. What is the product m1*m2?

Step 1: Identify the given equation, which is 2x^2 - 3xy + y^2 = 0.
Step 2: Recognize that this equation represents a pair of lines.
Step 3: In a general quadratic equation of the form ax^2 + bxy + cy^2 = 0, the product of the slopes (m1 * m2) of the lines can be found using the formula m1 * m2 = c/a.
Step 4: Identify the coefficients from the equation: a = 2 (coefficient of x^2), b = -3 (coefficient of xy), and c = 1 (coefficient of y^2).
Step 5: Substitute the values of c and a into the formula: m1 * m2 = c/a = 1/2.
Step 6: Calculate the product: m1 * m2 = 1/2 = 0.5.
Step 7: Note that the product of the slopes is positive, indicating the lines are not perpendicular.

Quadratic Equations – Understanding how to interpret a quadratic equation in two variables as representing two lines and how to extract information about their slopes.
Product of Slopes – Knowing that for a quadratic equation of the form ax^2 + bxy + cy^2 = 0, the product of the slopes of the lines is given by m1*m2 = c/a.