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The pair of lines represented by the equation 4x^2 - 12xy + 9y^2 = 0 are:

Practice Questions

Q1
The pair of lines represented by the equation 4x^2 - 12xy + 9y^2 = 0 are:
  1. Parallel
  2. Intersecting
  3. Coincident
  4. Perpendicular

Questions & Step-by-Step Solutions

The pair of lines represented by the equation 4x^2 - 12xy + 9y^2 = 0 are:
  • Step 1: Start with the equation 4x^2 - 12xy + 9y^2 = 0.
  • Step 2: Recognize that this is a quadratic equation in terms of x and y.
  • Step 3: Try to factor the equation. Look for two expressions that multiply to give the original equation.
  • Step 4: Notice that 4x^2 can be written as (2x)(2x) and 9y^2 as (3y)(3y).
  • Step 5: Rewrite the equation as (2x - 3y)(2x - 3y) = 0.
  • Step 6: This shows that both factors are the same, meaning the lines are coincident (they overlap completely).
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