Question:
The equation $3x²+7xy+2y²+5x+5y+2=0$ represents
The equation $3x²+7xy+2y²+5x+5y+2=0$ represents
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The equation $3x+5x+5y+2=0$ represents
Updated On: Apr 15, 2026
- a pair of straight lines
- a circle
- an ellipse
- a hyperbola
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The Correct Option is A
Solution and Explanation
Step 1: Concept
A general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of lines if the discriminant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.
Step 2: Analysis
Comparing coefficients: $a=3, h=7/2, b=2, g=5/2, f=5/2, c=2$.
Step 3: Evaluation
$\Delta = (3)(2)(2) + 2(5/2)(5/2)(7/2) - 3(5/2)^2 - 2(5/2)^2 - 2(7/2)^2$.
Calculating this value yields $\Delta = 0$.
Step 4: Conclusion
Since $\Delta = 0$, the equation represents a pair of straight lines.
Final Answer: (a)
A general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of lines if the discriminant $\Delta = abc + 2fgh - af^2 - bg^2 - ch^2 = 0$.
Step 2: Analysis
Comparing coefficients: $a=3, h=7/2, b=2, g=5/2, f=5/2, c=2$.
Step 3: Evaluation
$\Delta = (3)(2)(2) + 2(5/2)(5/2)(7/2) - 3(5/2)^2 - 2(5/2)^2 - 2(7/2)^2$.
Calculating this value yields $\Delta = 0$.
Step 4: Conclusion
Since $\Delta = 0$, the equation represents a pair of straight lines.
Final Answer: (a)
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