Question

If the lines \( \ell_1 : \ell m + mn + n = 0 \), \( \ell_2 : mn + m + n = 0 \) are concurrent then

• A. \( \ell = m = n = 0 \)
• B. \( \ell = m = n \)
• C. \( m \neq n \)
• D. \( \ell = m \neq n \)

Hint:

For concurrent lines, solve the system of equations to find the values of the parameters that make the lines meet at a single point.

Answer 1

The Correct Option is A

Step 1: Analyze the system of equations.
For the two lines to be concurrent, the system of equations must have a common solution. This happens when \( \ell = m = n = 0 \).
Step 2: Conclusion.
The lines are concurrent when \( \ell = m = n = 0 \). Final Answer: \[ \boxed{\ell = m = n = 0} \]