Question

To the lines \( ax^2 + 2hxy + by^2 = 0 \), the line \( ax^2 + 2h(a+b)xy + b^2y^2 = 0 \) are:

• A. equally inclined
• B. perpendicular
• C. bisector of the angle
• D. None of the above

Hint:

For two lines to be equally inclined, their angle between them must be 45°, and the coefficients should satisfy the condition for equal inclination.

Answer 1

The Correct Option is A

Step 1: Understand the condition for the lines.
When two lines are equally inclined, the angle between them is 45°. This condition holds when the coefficients of the lines are equal.
Step 2: Conclusion.
Thus, the lines are equally inclined.
Final Answer: \[ \boxed{A} \]