Question

Given below are two statements:
{Statement (I):} Two families of curves such that every member of either family cuts each member of the other family at right angles are called orthogonal trajectories of each other.
{Statement (II):} The orthogonal trajectories of the curve \( xy = c \) is \( y = \frac{1}{x} \).
Choose the most appropriate answer from the options given below:

• A. Both Statement I and Statement II are correct
• B. Both Statement I and Statement II are incorrect
• C. Statement I is correct but Statement II is incorrect
• D. Statement I is incorrect but Statement II is correct

Hint:

Orthogonal trajectories can be found by solving the differential equation of one family of curves, and then solving for the other family that satisfies the condition of orthogonality.

Answer 1

The Correct Option is A

The concept of orthogonal trajectories is correct in Statement (I), as two families of curves that intersect at right angles are indeed called orthogonal. For Statement (II), the orthogonal trajectory of the hyperbola \( xy = c \) is \( y = \frac{1}{x} \), which is correct.