Question

The normal at the point \( (t_1, t_2) \) on the parabola, cuts the parabola again at the point whose parameter is

• A. \( t_1 = t_2 \)
• B. \( t_2 = t_1 + 2 \)
• C. \( t_2 = t_1 + 1 \)
• D. None of these

Hint:

In parabolic geometry, the parameter of the point where the normal intersects the curve is given by \( t_2 = t_1 + 1 \).

Answer 1

The Correct Option is C

Step 1: Geometry of the Parabola.
For a parabola, the normal at any point intersects the curve again at a point whose parameter is related by \( t_2 = t_1 + 1 \). This can be derived using the geometry of the parabola.
Step 2: Conclusion.
The correct answer is (C), \( t_2 = t_1 + 1 \).