Question

The joint equation of the lines through the origin trisecting angles in the first and third quadrant is

• A. \( \sqrt{3} (x^2 - y^2) + 4xy = 0 \)
• B. \( \sqrt{3} (x^2 + y^2) - 4xy = 0 \)
• C. \( \sqrt{3} (x^2 + y^2) + 4xy = 0 \)
• D. \( \sqrt{3} (x^2 - y^2) - 4xy = 0 \)

Hint:

For trisecting lines, use the standard joint equation derived from the conditions of angle bisectors in the first and third quadrants.

Answer 1

The Correct Option is B

Step 1: Use the standard equation of trisecting lines.
The joint equation of the lines trisecting angles in the first and third quadrants is given by the equation: \[ \sqrt{3}(x^2 + y^2) - 4xy = 0 \]
Step 2: Conclusion.
Thus, the joint equation of the lines is \( \sqrt{3} (x^2 + y^2) - 4xy = 0 \).