Home
Class 12
MATHS
Find the orthogonal trajectories of fami...

Find the orthogonal trajectories of family of curves `x^2+y^2=c x`

Text Solution

Verified by Experts

The correct Answer is:
`x^(2)+y^(2)=k^(2)`
`x^(2)+y^(2)=cx`…………..(1)
Differentiating w.r.t x, we get `2x+2y(dy)/(dx)=c`……………(2)
Elliminating c between (1) and (2), we get
`2x+2y(dy)/(dx)=(x^(2)+y^(2))/(x)` or `(dy)/(dx) =(y^(2)-x^(2))/(2xy)`
Replacing `(dy)/(dx)by-(dx)/(dy)`, we get `(dy)/(dx)=(2xy)/(x^(2)-y^(2))`
This equation is homogeneous, and its solution gives the orthogonal trajectories as `x^(2)+y^(2)=ky`.
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.9|5 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise (Single)|74 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Exercise 10.7|5 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE|Exercise Exercise|337 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Numerical Value Type|3 Videos

Similar Questions

Explore conceptually related problems

Find the orthogonal trajectories of family of curves x^(2)+y^(2)=cx

Find the orthogonal trajectories of xy=c

Find the orthogonal trajectories of xy=c

Orthogonal trajectories of the family of curves x^2 + y^2 = c^2

The orthogonal trajectories of the family of curves y=Cx^(2) , (C is an arbitrary constant), is

STATEMENT-1 : The orthogonal trajectory of a family of circles touching x-axis at origin and whose centre the on y-axis is self orthogonal. and STATEMENT-2 : In order to find the orthogonal trajectory of a family of curves we put -(dx)/(dy) in place of (dy)/(dx) in the differential equation of the given family of curves.

If the orthogonal trajectories of the family of curves e^(n-1)x=y^(n) .(where e is a parameter) always passes through (1, e) and (0, 0) then value of n is

Orthogonal trajectories of the family of curves x^(2)+y^(2)=a is an arbitrary constant is