If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?
Practice Questions
1 question
Q1
If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?
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The product of the slopes of the lines can be found from the equation. Here, the product of the slopes is given by -c/a, where c is the coefficient of xy and a is the coefficient of x^2.
Questions & Step-by-step Solutions
1 item
Q
Q: If the lines represented by the equation 3x^2 + 2xy - y^2 = 0 intersect at the origin, what is the product of their slopes?
Solution: The product of the slopes of the lines can be found from the equation. Here, the product of the slopes is given by -c/a, where c is the coefficient of xy and a is the coefficient of x^2.
Steps: 6
Step 1: Identify the given equation, which is 3x^2 + 2xy - y^2 = 0.
Step 2: Recognize that this equation represents two lines that intersect at the origin (0,0).
Step 3: Identify the coefficients in the equation: a = 3 (coefficient of x^2), c = 2 (coefficient of xy).
Step 4: Use the formula for the product of the slopes of the lines, which is -c/a.
Step 5: Substitute the values into the formula: -c/a = -2/3.
Step 6: Calculate the result: The product of the slopes is -2/3.
