The pair of lines represented by the equation x^2 - 4xy + 3y^2 = 0 are:
Practice Questions
1 question
Q1
The pair of lines represented by the equation x^2 - 4xy + 3y^2 = 0 are:
Parallel
Perpendicular
Intersecting
Coincident
To determine the nature of the lines, we can find the slopes from the equation. The product of the slopes will help us conclude if they are perpendicular.
Questions & Step-by-step Solutions
1 item
Q
Q: The pair of lines represented by the equation x^2 - 4xy + 3y^2 = 0 are:
Solution: To determine the nature of the lines, we can find the slopes from the equation. The product of the slopes will help us conclude if they are perpendicular.
Steps: 8
Step 1: Start with the given equation: x^2 - 4xy + 3y^2 = 0.
Step 2: This equation is a quadratic in terms of x and y, which can be factored to find the slopes of the lines.
Step 3: Rewrite the equation in the standard form: (x - ay)(x - by) = 0, where a and b are the slopes.
Step 4: To factor, we need to find two numbers that multiply to 3 (the coefficient of y^2) and add to -4 (the coefficient of xy).
Step 5: The numbers that work are -3 and -1, so we can factor the equation as (x - 3y)(x - y) = 0.
Step 6: From the factored form, we can see the slopes of the lines are 3 and 1 (from x = 3y and x = y).
Step 7: To check if the lines are perpendicular, calculate the product of the slopes: 3 * 1 = 3.
Step 8: Since the product of the slopes is not -1, the lines are not perpendicular.
