Ordinary Differential Equations-Orthogonal Trajectory [IFS (Forest Services) Mathematics]: Questions 1 - 7 of 7

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Question 1

Appeared in Year: 2016 (IAS)

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Find the general equation of surface orthonormal to the family of spheres given by [CS (Main) Paper 2]

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Explanation

  • Given family of surface is

  • Here

… (147 more equations) …

Question 2

Appeared in Year: 2013 (IAS)

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Obtain an equation the orthogonal trajectory of the family of curve represented by being the plane polar coordinates. (CS Paper 1)

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Explanation

Given,

where a is parameter

… (263 more equations) …

Question 3

Appeared in Year: 2012 (IAS)

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Find the orthogonal trajectories of the family of curve (CS Paper 1)

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Explanation

Given,

Differentiating (1) w. r. t

Putting value of in equat…

… (580 more equations) …

Question 4

Appeared in Year: 2012 (IAS)

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Determine the Orthogonal trajectory of a family of curve represented by the polar equation

being the plane polar coordinates od any point. (CS Paper 1)

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Explanation

the given family of curve is

Taking logarithm on both sides of (1) , we get

… (137 more equations) …

Question 5

Appeared in Year: 2021 (IAS)

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Find the orthogonal trajectories of the family of curves is a parameter. (Paper -1)

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Explanation

Given

Differentiating,

… (77 more equations) …

Question 6

Appeared in Year: 2022 (IAS)

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Show that the orthogonal trajectories of the system of parabolas belong to the same system (Paper 1)

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Explanation

Given

Differentiate it with respect to y, we get

… (92 more equations) …

Question 7

Appeared in Year: 2020 (IAS)

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Find the orthogonal trajectories of the family of circles passing through the point and (Paper 1)

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Explanation

We know that

is known as family of circles

Given that it passes through and

… (686 more equations) …