For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, what is the prod

For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, what is the product of the slopes?

For the lines represented by the equation 2x^2 + 3xy + y^2 = 0, what is the product of the slopes?

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: To find the slopes of the lines, we can rewrite the equation in a standard form.
Step 4: The equation can be factored or analyzed to find the slopes directly.
Step 5: The product of the slopes of two lines represented by the equation ax^2 + bxy + cy^2 = 0 is given by the formula -c/a.
Step 6: In our case, a = 2 and c = 1, so we calculate -c/a = -1/2.
Step 7: Therefore, the product of the slopes is -1.

Quadratic Equations – Understanding how to interpret and manipulate quadratic equations to find properties such as slopes of lines.
Slopes of Lines – Knowledge of how to calculate the slopes of lines represented by a quadratic equation and the relationship between them.
Product of Slopes – Understanding the relationship between the coefficients of a quadratic equation and the product of the slopes of the lines it represents.