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The differential equation for the family of circle x²+y²-2ay=0, where a is an arbitrary constant is
- (x²+y²)y'=2xy
- 2(x²+y²)y'=xy
- (x²-y²)y'=2xy
- 2(x²-y²)y'=xy
Correct answer: (x²-y²)y'=2xy
Solution
The correct option represents the relationship between the variables in the equation of the circle by differentiating implicitly, leading to a form that captures the geometric properties of the circle while incorporating the variable change due to the arbitrary constant.
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