Question

Given below are two statements:
Assertion (A): If a curve cut every member of a given family of curves at right angle, it is called orthogonal trajectory.
Reason (R): For the orthogonal trajectory of a differential equation, the derivative \(\dfrac{dy}{dx}\) is replaced by \(-\dfrac{dx}{dy}\).

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

For orthogonal trajectories, replace slope \(m\) by \(-\frac{1}{m}\).

Answer 1

The Correct Option is A