Question

The separate equations of the lines represented by the equation \( 3x^2 - 2\sqrt{3} xy - 3y^2 = 0 \) are

• A. \( x - \sqrt{3} y = 0 \) and \( 3x + \sqrt{3} y = 0 \)
• B. \( x + \sqrt{3} y = 0 \) and \( 3x + \sqrt{3} y = 0 \)
• C. \( x - \sqrt{3} y = 0 \) and \( 3x - \sqrt{3} y = 0 \)
• D. \( x + \sqrt{3} y = 0 \) and \( 3x - \sqrt{3} y = 0 \)

Hint:

When given a quadratic equation in two variables, check if it can be factored into the product of two linear factors.

Answer 1

The Correct Option is A

Step 1: Factor the given equation.
The equation \( 3x^2 - 2\sqrt{3} xy - 3y^2 = 0 \) represents the product of two linear factors. By factoring, we get: \[ ( x - \sqrt{3} y ) ( 3x + \sqrt{3} y ) = 0 \] Step 2: Conclusion.
The separate equations are \( x - \sqrt{3} y = 0 \) and \( 3x + \sqrt{3} y = 0 \), so the correct answer is (A).