Question

If the normal to the rectangular hyperbola \( xy = c^2 \) at the point \( (ct, c/t) \) meets the curve again at \( (ct', c/t') \), then:

• A. \( t' + t = 1 \)
• B. \( t' = -t \)
• C. \( t' = t - 1 \)
• D. \( t' = 1 \)

Hint:

The normal to a curve often intersects the curve at a point where the parameter \( t' \) is related to \( t \) in a simple way, often as \( t' = -t \).

Answer 1

The Correct Option is B

Step 1: Use properties of the normal. The normal to the rectangular hyperbola intersects the curve again at the point where the value of \( t' \) is the negative of \( t \).
Step 2: Conclusion. Thus, \( t' = -t \).