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Determine the condition for the lines represented by the equation 4x^2 + 4xy + y
Determine the condition for the lines represented by the equation 4x^2 + 4xy + y^2 = 0 to be coincident.
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Practice Questions
1 question
Q1
Determine the condition for the lines represented by the equation 4x^2 + 4xy + y^2 = 0 to be coincident.
b^2 - 4ac = 0
b^2 - 4ac > 0
b^2 - 4ac < 0
b^2 - 4ac = 1
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For the lines to be coincident, the discriminant must be zero, i.e., b^2 - 4ac = 0.
Questions & Step-by-step Solutions
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Q
Q: Determine the condition for the lines represented by the equation 4x^2 + 4xy + y^2 = 0 to be coincident.
Solution:
For the lines to be coincident, the discriminant must be zero, i.e., b^2 - 4ac = 0.
Steps: 6
Show Steps
Step 1: Start with the given equation: 4x^2 + 4xy + y^2 = 0.
Step 2: Identify the coefficients in the standard form of a quadratic equation Ax^2 + Bxy + Cy^2 = 0. Here, A = 4, B = 4, and C = 1.
Step 3: Write down the formula for the discriminant: D = B^2 - 4AC.
Step 4: Substitute the values of A, B, and C into the discriminant formula: D = (4)^2 - 4(4)(1).
Step 5: Calculate the discriminant: D = 16 - 16 = 0.
Step 6: Since the discriminant is zero, this means the lines represented by the equation are coincident.
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