Question

If \( 4a^2 + b^2 + 2c^2 + 4ab - 6ac - 3bc = 0 \), the family of lines \( ax + by + c = 0 \) is concurrent at one or the other of the two points-

• A. \( (-1, -1) \), \( (2, -1) \)
• B. \( (-1, 1) \), \( (-2, -1) \)
• C. \( (-1, 2) \), \( (-2, 1) \)
• D. \( (-1, -1) \), \( (1, -1) \)

Hint:

For a family of concurrent lines, solving the corresponding system of equations will give the points of concurrency.

Answer 1

The Correct Option is A

Step 1: Analyze the equation.
The given equation represents a condition for the concurrent lines, and solving it gives the points of concurrency.
Step 2: Conclusion.
The points of concurrency are \( (-1, -1) \) and \( (2, -1) \). Final Answer: \[ \boxed{(-1, -1), (2, -1)} \]