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Question

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


Solution



The equation of the family of circle having centre on Y-axis and radius 3 units is 
x2+(yb)2=9         ...(i)
On differentiating Eq. (i) w.r.t. x, we get
2x+2(yb)y=0yb=xy        ...(ii)
On substituting this value of (y-b) in Eq. (i), we get
x2+(xy)2=9x2[(y)2+1]=8(y)2(x29)(y)2+x2=0
which is the required differential equation.

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