Question

The straight lines represented by the equation \( 9x^2 - 12xy + 4y^2 = 0 \) are

• A. coincident
• B. perpendicular
• C. intersect at 60°
• D. parallel

Hint:

For equations of the form \( Ax^2 + 2Bxy + Cy^2 = 0 \), the lines are perpendicular if \( B^2 - AC = 0 \).

Answer 1

The Correct Option is B

Step 1: Recognize the conic equation.
The given equation represents a pair of straight lines. We can rewrite it in the form \( (Ax + By)(Cx + Dy) = 0 \), which represents the equation of two straight lines. To determine the angle between the lines, we use the condition for perpendicularity. In this case, the lines are perpendicular.

Step 2: Conclusion.
Thus, the lines are perpendicular, corresponding to option (B).