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?
Practice Questions
1 question
Q1
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?
-2
1
3/2
0
The product of the slopes of the lines is given by m1*m2 = c/a = 1/2 = -2.
Questions & Step-by-step Solutions
1 item
Q
Q: 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?
Solution: The product of the slopes of the lines is given by m1*m2 = c/a = 1/2 = -2.
Steps: 7
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.
