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Form the differential equation of the f...

Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

Text Solution

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`C:(0,K)`
`C:(x-0)^2+(yk)^2=9` -(1)
differentiate with respect to x
`C':2x+2(y-k)*y'=0`
`(y-k)=-x/y'`
putting this value in equation (1)
`x^2+x^2/(y'^2)=9`
`(xy')^2+x^2=(3y')^2`
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