Class 12

Math

Calculus

Differential Equations

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

$C:(x−0)_{2}+(yk)_{2}=9$ -(1)

differentiate with respect to x

$C_{′}:2x+2(y−k)⋅y_{′}=0$

$(y−k)=−yx _{′}$

putting this value in equation (1)

$x_{2}+y_{′2}x_{2} =9$

$(xy_{′})_{2}+x_{2}=(3y_{′})_{2}$