Question

If \( l \) and \( m \) are the order and degree of the differential equation of all the straight lines at constant distance \( P \) units from the origin, then \[ lm^2 + l^2 m = \]

• A. 2
• B. 6
• C. 12
• D. 30

Hint:

Convert geometric condition into differential form to determine order and degree.

Answer 1

The Correct Option is A

The general form is distance from origin to line = \( P \), i.e., \( \frac{|Ax + By + C|}{\sqrt{A^2 + B^2}} = P \). This leads to a differential equation of order 1 and degree 1. Hence, \( l = 1 \), \( m = 1 \), \[ lm^2 + l^2 m = 1 \cdot 1 + 1 \cdot 1 = 2 \]