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The pair of lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are:
The pair of lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are:
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Practice Questions
1 question
Q1
The pair of lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are:
Real and distinct
Imaginary
Coincident
Real and coincident
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The discriminant of the quadratic equation is negative, indicating imaginary lines.
Questions & Step-by-step Solutions
1 item
Q
Q: The pair of lines represented by the equation 5x^2 + 6xy + 5y^2 = 0 are:
Solution:
The discriminant of the quadratic equation is negative, indicating imaginary lines.
Steps: 10
Show Steps
Step 1: Identify the equation given, which is 5x^2 + 6xy + 5y^2 = 0.
Step 2: Recognize that this is a quadratic equation in two variables (x and y).
Step 3: To analyze the lines represented by this equation, we need to calculate the discriminant.
Step 4: The discriminant (D) for a quadratic equation of the form Ax^2 + Bxy + Cy^2 = 0 is given by the formula D = B^2 - 4AC.
Step 5: In our equation, A = 5, B = 6, and C = 5.
Step 6: Substitute these values into the discriminant formula: D = 6^2 - 4(5)(5).
Step 7: Calculate 6^2, which is 36.
Step 8: Calculate 4(5)(5), which is 100.
Step 9: Now, subtract: D = 36 - 100 = -64.
Step 10: Since the discriminant is negative (D < 0), this indicates that the lines represented by the equation are imaginary.
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