Question

The angle between the tangents at those points on the curve \( x = t^2 + 1 \) and \( y = t^2 - t - 6 \) where it meets the x-axis is

• A. \( \pm \tan^{-1} \left( \frac{4}{29} \right) \)
• B. \( \pm \tan^{-1} \left( \frac{5}{49} \right) \)
• C. \( \pm \tan^{-1} \left( \frac{10}{49} \right) \)
• D. \( \pm \tan^{-1} \left( \frac{8}{29} \right) \)

Hint:

The angle between tangents can be found using the slopes of the tangents at the points of intersection.

Answer 1

The Correct Option is C

Step 1: Equation of tangents.
Use the parametric equations to find the derivatives of the curve to obtain the slopes of the tangents at the points where the curve intersects the x-axis. Then calculate the angle between the tangents.

Step 2: Conclusion.
Thus, the correct answer is option (C).

Final Answer: \[ \boxed{\text{(C) } \pm \tan^{-1} \left( \frac{10}{49} \right)} \]