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Question
Form the differential equation of the family of circles having centre on y-axis and radius 3 units.
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Solution
Let the centre of the circle on y-axis be (0, b).
The differential equation of the family of circles with centre at (0, b) and radius 3 is as follows:
`x^2+(y - b)^2 = 3^2`
Differentiating equation (1) with respect to x, we get:
This is the required differential equation.
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