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The differential equation for the family of curves x2+ y2 - 2ay = 0, where a is an arbitrary constant is
  • a)
    (x2 - y2)y′ = 2xy
  • b)
    2(x2 + y2)y′ = xy
  • c)
    2(x2 - y2)y′ = xy
  • d)
    (x2 + y2)y′ = 2xy
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The differential equation for the family of curves x2+ y2 - 2ay = 0, w...
The given family of curves can be rewritten as:

x^2 - 2ay = -y^2

Differentiating both sides with respect to x, we get:

2x - 2ay' = -2yy'

Simplifying and rearranging, we get:

(2x - 2ay')/(-2y) = y'

Dividing both sides by x, we get:

(2 - 2ay'/x)/(y/x) = y'/x

Simplifying and rearranging, we get:

y'/x = (2y)/(2a - x)

This is the required differential equation for the family of curves x^2 - y^2 - 2ay = 0.
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The differential equation for the family of curves x2+ y2 - 2ay = 0, w...
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The differential equation for the family of curves x2+ y2 - 2ay = 0, where a is an arbitrary constant isa)(x2 - y2)y′ = 2xyb)2(x2 + y2)y′ = xyc)2(x2 - y2)y′ = xyd)(x2 + y2)y′ = 2xyCorrect answer is option 'A'. Can you explain this answer?
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The differential equation for the family of curves x2+ y2 - 2ay = 0, where a is an arbitrary constant isa)(x2 - y2)y′ = 2xyb)2(x2 + y2)y′ = xyc)2(x2 - y2)y′ = xyd)(x2 + y2)y′ = 2xyCorrect answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The differential equation for the family of curves x2+ y2 - 2ay = 0, where a is an arbitrary constant isa)(x2 - y2)y′ = 2xyb)2(x2 + y2)y′ = xyc)2(x2 - y2)y′ = xyd)(x2 + y2)y′ = 2xyCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The differential equation for the family of curves x2+ y2 - 2ay = 0, where a is an arbitrary constant isa)(x2 - y2)y′ = 2xyb)2(x2 + y2)y′ = xyc)2(x2 - y2)y′ = xyd)(x2 + y2)y′ = 2xyCorrect answer is option 'A'. Can you explain this answer?.
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