Question

Diffrential equation of all circle with center on"- axis

Answer 1

Answer:

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Step-by-step explanation:

All circles passing through origin and having centre on X−axis say at (a,0) will have radius=a

∴ General equation of such circles is

(x−a)2+y2=a2..........(i)

This equation has only one arbitrary constant.a.

∴ This equation can be differentiated only once to remove the arbitrary constant a

Differentiating (i) on both the sides we get

2(x−a)+2y.dy/dx=0........(ii)

⇒x−a=−y.dydx

and

a=x+ydy/dx

Substituting the values of (x−a)anda in (i) we get

y2.(dy/dx)2+y2=(x+ydy/dx)2

⇒y2.(dy/dx)2+y2=x2+y2.(dy/dx)2+2xy.dy/dx

⇒y2=x2+2xy.dy/dx

is the differential equation of the given circles.

Answer 2

Answer:

Step-by-step explanation: