Question

Write the separate equations of lines represented by the equation \( x^2 - 9y^2 = 0 \)

Hint:

Factorize homogeneous equations like \( x^2 - 9y^2 = 0 \) to find individual line equations.

Answer 1

Rewrite: \( x^2 - 9y^2 = (x - 3y)(x + 3y) = 0 \). 
The equation represents two lines: 
1. \( x - 3y = 0 \Rightarrow x = 3y \Rightarrow y = \frac{x}{3} \). 
2. \( x + 3y = 0 \Rightarrow x = -3y \Rightarrow y = -\frac{x}{3} \). 
Answer: \( x - 3y = 0 \), \( x + 3y = 0 \).