Find the angle between the lines represented by the equation 2x^2 - 3xy + y^2 = 0.
Practice Questions
1 question
Q1
Find the angle between the lines represented by the equation 2x^2 - 3xy + y^2 = 0.
30 degrees
45 degrees
60 degrees
90 degrees
The angle between the lines can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes of the lines. The slopes can be found from the equation.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the angle between the lines represented by the equation 2x^2 - 3xy + y^2 = 0.
Solution: The angle between the lines can be found using the formula tan(θ) = |(m1 - m2) / (1 + m1*m2)|, where m1 and m2 are the slopes of the lines. The slopes can be found from the equation.
Steps: 11
Step 1: Start with the given equation of the lines: 2x^2 - 3xy + y^2 = 0.
Step 2: Recognize that this is a quadratic equation in x and y, which represents two lines.
Step 3: To find the slopes of the lines, we need to factor the equation or use the quadratic formula.
Step 4: Rewrite the equation in the form of ax^2 + bxy + cy^2 = 0, where a = 2, b = -3, c = 1.
Step 5: Use the formula for the slopes of the lines: m1, m2 = [(-b ± √(b^2 - 4ac)) / (2a)].
