Question

If the equation \( ax^2 + hy^2 + cx + cy = 0, c \neq 0 \) represents a pair of lines, then

• A. \( a + c = 0 \)
• B. \( a + b = 0 \)
• C. \( a - c = 0 \)
• D. \( a - b = 0 \)

Hint:

For the equation \( ax^2 + hy^2 + cx + cy = 0 \) to represent a pair of lines, the condition is \( a + b = 0 \).

Answer 1

The Correct Option is B

Step 1: Condition for a pair of lines.
For the equation \( ax^2 + hy^2 + cx + cy = 0 \) to represent a pair of straight lines, the condition is \( a + b = 0 \), where \( a \), \( b \), and \( c \) are constants in the equation.
Step 2: Conclusion.
Thus, the correct answer is \( a + b = 0 \), corresponding to option (B).