JEE Exam > JEE Questions > Differential equation of the family of parabo...
Start Learning for Free
Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis is
- a)xy′ – 2y = 0
- b)xy′ + 2y = 0
- c)y′ – 2y = 0
- d)xy′2 + 2y = 0
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Differential equation of the family of parabolas having vertex at orig...
Most Upvoted Answer
Differential equation of the family of parabolas having vertex at orig...
Family of Parabolas with Vertex at Origin and Axis along Positive y-axis
To find the differential equation of the family of parabolas with vertex at the origin and axis along the positive y-axis, we first need to consider the general equation of a parabola in this form:
y = ax^2
where 'a' is a parameter that varies for different parabolas in the family.
Deriving the Differential Equation
1. Differentiate the general equation of the parabola with respect to x:
y' = 2ax
2. Since the vertex is at the origin, the vertex of the parabola is at (0,0). Therefore, the equation passes through the origin.
3. Substituting the vertex point into the equation of the parabola:
0 = a(0)^2
0 = 0
This implies that a = 0
4. Therefore, the equation of the parabola in the family is y = 0, which simplifies to y = 0x^2.
Writing the Differential Equation
1. Substitute y = 0 into the differentiated equation:
y' = 2(0)x
y' = 0
2. The differential equation for the family of parabolas with vertex at the origin and axis along the positive y-axis is:
xy' - 2y = 0
Therefore, the correct answer is option 'a': xy' - 2y = 0.
To find the differential equation of the family of parabolas with vertex at the origin and axis along the positive y-axis, we first need to consider the general equation of a parabola in this form:
y = ax^2
where 'a' is a parameter that varies for different parabolas in the family.
Deriving the Differential Equation
1. Differentiate the general equation of the parabola with respect to x:
y' = 2ax
2. Since the vertex is at the origin, the vertex of the parabola is at (0,0). Therefore, the equation passes through the origin.
3. Substituting the vertex point into the equation of the parabola:
0 = a(0)^2
0 = 0
This implies that a = 0
4. Therefore, the equation of the parabola in the family is y = 0, which simplifies to y = 0x^2.
Writing the Differential Equation
1. Substitute y = 0 into the differentiated equation:
y' = 2(0)x
y' = 0
2. The differential equation for the family of parabolas with vertex at the origin and axis along the positive y-axis is:
xy' - 2y = 0
Therefore, the correct answer is option 'a': xy' - 2y = 0.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Question Description
Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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 Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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 Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer?.
Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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 Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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 Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer?.
Solutions for Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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 Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Differential equation of the family of parabolas having vertex at origin and axis along positive y-axis isa)xy′ – 2y = 0b)xy′ + 2y = 0c)y′ – 2y = 0d)xy′2+2y=0Correct 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