Question

The absolute value of the tangent of the difference of the angles made by the lines \( 4x^2 - 24xy + 11y^2 = 0 \) with the X-axis is:

• A. \( \frac{4}{11} \)
• B. \( \frac{24}{11} \)
• C. \( \frac{4}{3} \)
• D. \( \frac{11}{24} \)

Hint:

For equations involving the tangent of angle differences, use the formula for the slope and the relation for the angle between two lines.

Answer 1

The Correct Option is C

To find the tangent of the difference of the angles, we need to find the slopes of the lines. For the quadratic equation given, we use the angle formula and the fact that the lines are symmetric to get \( \frac{4}{3} \).