Ordinary Differential Equations-Orthogonal Trajectory [IAS (Admin.) Mains Mathematics]: Questions 1 - 7 of 7
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Question 1
Appeared in Year: 2016
Describe in Detail Subjective▾
Find the general equation of surface orthonormal to the family of spheres given by [CS (Main) Paper 2]
EditExplanation
- Given family of surface is
- Here
… (147 more equations) …
Question 2
Appeared in Year: 2013
Describe in Detail Subjective▾
Obtain an equation the orthogonal trajectory of the family of curve represented by being the plane polar coordinates. (CS Paper 1)
EditExplanation
Given,
where a is parameter
… (263 more equations) …
Question 3
Appeared in Year: 2012
Describe in Detail Subjective▾
Find the orthogonal trajectories of the family of curve (CS Paper 1)
EditExplanation
Given,
Differentiating (1) w. r. t
Putting value of in equat…
… (580 more equations) …
Question 4
Appeared in Year: 2012
Describe in Detail Subjective▾
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)
EditExplanation
the given family of curve is
Taking logarithm on both sides of (1) , we get
… (137 more equations) …
Question 5
Appeared in Year: 2021
Describe in Detail Subjective▾
Find the orthogonal trajectories of the family of curves is a parameter. (Paper -1)
EditExplanation
Given
Differentiating,
… (77 more equations) …
Question 6
Appeared in Year: 2022
Describe in Detail Subjective▾
Show that the orthogonal trajectories of the system of parabolas belong to the same system (Paper 1)
EditExplanation
Given
Differentiate it with respect to y, we get
… (92 more equations) …
Question 7
Appeared in Year: 2020
Describe in Detail Subjective▾
Find the orthogonal trajectories of the family of circles passing through the point and (Paper 1)
EditExplanation
We know that
is known as family of circles
Given that it passes through and
… (686 more equations) …