Question

If the equation \[ ax^2 + hxy + by^2 = 0, \quad c \neq 0 \text{ represents a pair of coincident lines, then} \]

• A. \( h^2 = 2ab \)
• B. \( h^2 = 4ab \)
• C. \( h^2 = 8ab \)
• D. \( h^2 = ab \)

Hint:

For the general second-degree equation representing a pair of coincident lines, use the condition \( h^2 = 4ab \).

Answer 1

The Correct Option is B

Step 1: Condition for a pair of coincident lines.
For the equation \( ax^2 + hxy + by^2 = 0 \) to represent a pair of coincident lines, the condition is \( h^2 = 4ab \).
Step 2: Conclusion.
Thus, the condition for the equation to represent a pair of coincident lines is \( h^2 = 4ab \), corresponding to option (B).