The pair of straight lines represented by the equation x^2 - 4xy + y^2 = 0 are:

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Question: The pair of straight lines represented by the equation x^2 - 4xy + y^2 = 0 are:

Options:

Correct Answer: Perpendicular

Solution:

The given equation can be factored as (x - 2y)(x - 2y) = 0, indicating that the lines are perpendicular.

The pair of straight lines represented by the equation x^2 - 4xy + y^2 = 0 are:

The pair of straight lines represented by the equation x^2 - 4xy + y^2 = 0 are:

Step 1: Start with the given equation: x^2 - 4xy + y^2 = 0.
Step 2: Recognize that this is a quadratic equation in terms of x and y.
Step 3: Try to factor the equation. Look for two expressions that multiply to give the original equation.
Step 4: Notice that the equation can be factored as (x - 2y)(x - 2y) = 0.
Step 5: This means that both lines represented by the equation are the same line, which is x - 2y = 0.
Step 6: The line x - 2y = 0 can be rewritten as y = (1/2)x, which indicates the slope of the line.
Step 7: Since we have a repeated factor, the lines are not distinct but rather the same line, and they are not perpendicular.

Pair of Straight Lines – Understanding how to identify and analyze the equations representing pairs of straight lines in a coordinate plane.
Factoring Quadratic Equations – The ability to factor quadratic equations to find the roots or lines represented by the equation.
Perpendicular Lines – Recognizing the conditions under which two lines are perpendicular based on their slopes or factored forms.