If the lines `lx+2y +3=0` and `2y+mx+4=0` cut the co-ordinate axes in concylic points then lm=

Options

A. 4
B. `-4`
C. 2
D. 8

Answer

To solve the problem, we need to determine the value of \( lm \) given that the lines \( lx + 2y + 3 = 0 \) and \( 2y + mx + 4 = 0 \) cut the coordinate axes at concyclic points.

### Step-by-Step Solution:

1. **Identify the coefficients of the lines**:
- For the first line \( lx + 2y + 3 = 0 \):
- \( a_1 = l \), \( b_1 = 2 \), \( c_1 = 3 \)
- For the second line \( 2y + mx + 4 = 0 \):
- Rearranging gives \( mx + 2y + 4 = 0 \), so:
- \( a_2 = m \), \( b_2 = 2 \), \( c_2 = 4 \)

2. **Use the condition for concyclic points**:
- The condition for the points where the lines cut the axes to be concyclic is given by the formula:
\[ a_1 a_2 = b_1 b_2 \]
- Substituting the values:
\[ l \cdot m = 2 \cdot 2 \]
- This simplifies to:
\[ lm = 4 \]

3. **Conclusion**:
- Thus, the value of \( lm \) is \( 4 \).

### Final Answer:
\[ lm = 4 \]