The lines represented by the equation 4x^2 - 12xy + 9y^2 = 0 are:
Correct Answer: The lines are perpendicular.
- Step 1: Start with the given equation: 4x^2 - 12xy + 9y^2 = 0.
- Step 2: Recognize that this is a quadratic equation in terms of x and y, which can represent two lines.
- Step 3: Rewrite the equation in the standard form of a conic section, which is Ax^2 + Bxy + Cy^2 = 0.
- Step 4: Identify the coefficients: A = 4, B = -12, C = 9.
- Step 5: Use the formula to find the slopes of the lines: m1, m2 = (B ± √(B^2 - 4AC)) / (2A).
- Step 6: Calculate B^2 - 4AC: (-12)^2 - 4(4)(9) = 144 - 144 = 0.
- Step 7: Since B^2 - 4AC = 0, this means the lines are coincident (the same line) and not distinct.
- Step 8: Therefore, we cannot find two different slopes to check if they are perpendicular.
No concepts available.
