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Question
Form the differential equation of the family of circles touching the y-axis at the origin.
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Solution
The centre of the circle touching the y-axis at origin lies on the x-axis.
Let (a, 0) be the centre of the circle.
Since it touches the y-axis at origin, its radius is a.
Now, the equation of the circle with centre (a, 0) and radius (a) is
This is the required differential equation.
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