Q10 asap Q 10 Form the differential equation of the family of circles touching the x-axis at origin - Maths - Differential Equations

Question

Q10 asap
Q 10 Form the differential equation of the family of circles
touching the x-axis at origin

Aarushi Mishra · Accepted Answer

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Equation of a general circle is given byx-a2+y-b2=r2If the circle touches x-axis at origion then its center will lie along y-axis, let the center be 0,k, then also its radiuis will bekEquation becomesx-02+y-k2=k2x2+y2+k2-2ky=k2x2+y2-2ky=0_____________1d dx x2+y2-2ky=02x+2ydydx-2kdydx=0x+ydydx-kdydx=0k=x+ydydxdydxPut in equation 1x2+y2-2x+ydydxdydxy=0x2+y2dydx-2xy-2y2dydx=0x2-y2dydx-2xy=0

Q10 asap Q.10. Form the differential equation of the family of circles touching the x-axis at origin.

Q10 asap
Q.10. Form the differential equation of the family of circles touching the x-axis at origin.