Sanjay Gupta, Dev Samaj College For Women,Ferozepur City CHAPTER - 4
ORTHOGONAL TRAJECTORIES EXERCISE 4.1
Q.1
Q.2
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Q.3
Q.4
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Q.5
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Q.6
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Q.7
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Q.8
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Q.9
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Q.10
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Q.11
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Q.12
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Q.13
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Q.14
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Q.15
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Q.16
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Q.17
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Sanjay Gupta, Dev Samaj College For Women,Ferozepur City WORKING RULE FOR FINDING THE ORTHOGONAL TRAJECTORIES OF ONE PARAMETER FAMILY OF CURVES Family of Curves Cartesian Form ( x, y, c) 0 …………….(1)
Form Diff. Equation of (1) dy f ( x, y, ) 0 ……………….(3) dx
Polar Form (r, , c) 0 ……………. (2)
Form Diff. Equation of (2) dr f (r , , ) 0 ………………(4) d
For Orthogonal Trajectories of (1), dx dy Replace by in (3) dy dx
For Trajectories of (1), y tan in (3) Replace y by 1 y tan
For Orthogonal Trajectories of (2), dr 2 d Replace in (4) by r d dr
Diff. Equation of Orthogonal Trajectories of (1) dx f ( x, y, ) 0 …………..(*) dy
Diff. Equation of Trajectories of (1) y tan f ( x, y , ) 0 …………..(*) 1 y tan
Diff. Equation of Orthogonal Trajectories of (2) d f ( r , , r 2 ) 0 …………..(*) dr
Solve the Diff. Equation (*) Orthogonal or - Trajectories of (1) or (2)
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