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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, ...
= 2axy
b) (y2 - x2)y = 2axy
c) (x2 + y2)y = 2axy
d) (y2 - x2)x = 2axy

To find the differential equation for the given family of curves, we need to differentiate the given equation with respect to x and y separately and then eliminate the arbitrary constant a.

Differentiating x2 y2 - 2ay = 0 with respect to x, we get:

2xy2 - 2a(dy/dx) = 0

Simplifying, we get:

dy/dx = (xy2)/a

Differentiating x2 y2 - 2ay = 0 with respect to y, we get:

2x2y - 2a = 2xy(dy/dx)

Substituting the value of dy/dx from the previous equation, we get:

2x2y - 2a = 2x(y2/a)

Simplifying, we get:

y(x2 - y2/a) = a

Eliminating the arbitrary constant a, we get:

x2y - y3 = C, where C is a constant.

Therefore, the differential equation for the family of curves x2 y2 - 2ay = 0 is (y2 - x2)x = 2axy. The correct option is (d).
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The differential equation for the family of curves x2 + y2 - 2ay = 0, ...
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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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