JEE Exam > JEE Questions > If the differential equation of all the strai...
Start Learning for Free
If the differential equation of all the straight lines which are at a fixed distance of 10 units from the origin is given by (y − xy1)2 = A(1 + y12) then the value of A is equal to
- a)100
- b)10
- c)25
- d)50
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If the differential equation of all the straight lines which are at a ...
The given family of lines can be represented by the equation,
xcosα + ysin α = 10 ...(1)
where α is an arbitrary constant.
Differentiating we have,
cosα + sinαy1 = 0 ...(2)
Multiplying (2) by x and subtracting it from (1),
⇒ (y − xy1)sinα = 10 ...(3)
Multiplying (1) by y1 and (2) by y and subtracting,
xy1cosα − ycosα = 10y1
⇒ (xy1 − y)cosα = 10y1...(4)
Squaring and adding (3) and (4) we get, (y − xy1)2 = 100(1 + y12)
Now on comparing, we get A = 100.
xcosα + ysin α = 10 ...(1)
where α is an arbitrary constant.
Differentiating we have,
cosα + sinαy1 = 0 ...(2)
Multiplying (2) by x and subtracting it from (1),
⇒ (y − xy1)sinα = 10 ...(3)
Multiplying (1) by y1 and (2) by y and subtracting,
xy1cosα − ycosα = 10y1
⇒ (xy1 − y)cosα = 10y1...(4)
Squaring and adding (3) and (4) we get, (y − xy1)2 = 100(1 + y12)
Now on comparing, we get A = 100.
Free Test
FREE
| Start Free Test |
Community Answer
If the differential equation of all the straight lines which are at a ...
Given differential equation:
The given differential equation is (y - xy')^2 = A(1 + y'^2), where y' represents dy/dx.
Finding the value of A:
To find the value of A, we need to compare the given differential equation with the general equation of straight lines at a fixed distance from the origin.
The general equation of straight lines at a fixed distance 'd' from the origin is of the form: xcosθ + ysinθ = ±d.
Comparing the given differential equation with the general equation, we get:
- Comparing y - xy' with y, we get cosθ = 1.
- Comparing -xy' with sinθ, we get sinθ = -1.
- Therefore, cosθ = 1 and sinθ = -1, which implies θ = 180 degrees.
- Substituting θ = 180 degrees into the general equation, we get xcos180 + ysin180 = ±10.
- This simplifies to -x + y = ±10, which can be written as y = x ± 10.
Comparing this with the given differential equation, we get:
(y - xy')^2 = A(1 + y'^2) becomes (x ± 10)^2 = A(1 + 1) => x^2 ± 20x + 100 = 2A.
By comparing the coefficients, we find that A = 100.
Therefore, the value of A is 100.
The given differential equation is (y - xy')^2 = A(1 + y'^2), where y' represents dy/dx.
Finding the value of A:
To find the value of A, we need to compare the given differential equation with the general equation of straight lines at a fixed distance from the origin.
The general equation of straight lines at a fixed distance 'd' from the origin is of the form: xcosθ + ysinθ = ±d.
Comparing the given differential equation with the general equation, we get:
- Comparing y - xy' with y, we get cosθ = 1.
- Comparing -xy' with sinθ, we get sinθ = -1.
- Therefore, cosθ = 1 and sinθ = -1, which implies θ = 180 degrees.
- Substituting θ = 180 degrees into the general equation, we get xcos180 + ysin180 = ±10.
- This simplifies to -x + y = ±10, which can be written as y = x ± 10.
Comparing this with the given differential equation, we get:
(y - xy')^2 = A(1 + y'^2) becomes (x ± 10)^2 = A(1 + 1) => x^2 ± 20x + 100 = 2A.
By comparing the coefficients, we find that A = 100.
Therefore, the value of A is 100.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer?
Question Description
If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer?.
If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer?.
Solutions for If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If the differential equation of all the straight lines which are at a fixed distance of10 units from the origin is given by(y − xy1)2 = A(1 + y12) then the value ofA is equal toa)100b)10c)25d)50Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup