Question: The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
Options:
Discriminant > 0
Discriminant = 0
Discriminant < 0
None of the above
Correct Answer: Discriminant = 0
Solution:
For the lines to be coincident, the discriminant must be equal to zero.
The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to b
Practice Questions
Q1
The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
Discriminant > 0
Discriminant = 0
Discriminant < 0
None of the above
Questions & Step-by-Step Solutions
The condition for the lines represented by the equation x^2 + 2xy + y^2 = 0 to be coincident is:
Step 1: Start with the equation x^2 + 2xy + y^2 = 0.
Step 2: Recognize that this equation represents a pair of lines.
Step 3: To find the condition for the lines to be coincident, we need to use the concept of the discriminant.
Step 4: The discriminant is a value that helps us determine the nature of the roots of a quadratic equation.
Step 5: For the lines to be coincident, the discriminant must be equal to zero.
Step 6: Calculate the discriminant for the given equation and set it to zero to find the condition.
Quadratic Equations – Understanding how to analyze the discriminant of a quadratic equation to determine the nature of its roots.
Coincident Lines – Recognizing the condition under which two lines represented by a quadratic equation are coincident (i.e., they overlap completely).
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