Integral University B.Tech Admissions 2024
ApplyNAAC A+ Accredited | Highest CTC 12 LPA | Scholarships Available
16 Questions around this concept.
Suppose that a family of curves f (x, y, a) = 0 is given. A curve that intersects every member of this family of curves at 90o, then it is called an orthogonal trajectory of the given family of curves.
Consider the family of all circles having their center at origin (a few such circles appear in figure below)
The orthogonal trajectories for this family of circles would be members of the family of straight lines passing through the origin (shown by dashed lines).
Steps for finding Orthogonal Trajectory :
The equation of the family of curves is f(x, y, a) = 0, where ‘a’ is an arbitrary constant. Differentiate ‘f’ with respect to ‘x’ and eliminate ‘a’.
The differential equation you get in step 1, substitute, . This will give the differential equation of the orthogonal trajectory.
By solving this differential equation, we get the required orthogonal trajectory.
Illustration:
The orthogonal trajectories of the family y = x + ce-x
Differentiation of the given equation gives
"Stay in the loop. Receive exam news, study resources, and expert advice!"
Mathematics for Joint Entrance Examination JEE (Advanced) : Calculus
Page No. : 10.17
Line : 11
July 04, 2019
3323+ Downloads
638+ Downloads
8221+ Downloads
20278+ Downloads
8504+ Downloads
171540+ Downloads
7173+ Downloads
3888+ Downloads
7253+ Downloads
7271+ Downloads
NAAC A+ Accredited | Highest CTC 12 LPA | Scholarships Available
Ranked #46 among universities in India by NIRF | Highest CTC 50 LPA | 100% Placements
India's youngest NAAC A++ accredited University | NIRF rank band 151-200 | 2200 Recruiters | 45.98 Lakhs Highest Package
60+ Years of Education Legacy | UGC & AICTE Approved | Prestigious Scholarship Worth 6 Crores | H-CTC 35 LPA
India's Largest University | NAAC A++ Accredited | 100% Placement Record | Highest Package Offered : 3 Cr PA
Hands on Mentoring and Code Coaching | Cutting Edge Curriculum with Real World Application