Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
178k views
in Differential equations by (36.3k points)

Find the orthogonal trajectories of the family of curves x2 – y2 = c2.

1 Answer

+1 vote
by (33.0k points)
selected by
 
Best answer

The given curve is

x2 – y2 = c

2x - 2y(dy/dx) = 0

(dy/dx) = x/y

Replacing dy/dx by – dx/dy, we get

-dx/dy = x/y

(dx/x) + (dy/y) = 0

Integrating, we get 

log |x| + log |y| = log (c2

xy = c2

which is the required orthogonal trajectories.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...