dxdy=βx−y(2α+β)+4α(2+α)x−βy+2βxdy−(2α+β)ydy+4αdy=(2+α)xdx−βydx+2dxβ(xdy+ydx)−(2α+β)ydy+4αdy=(2+α)xdx+2dxβxy−2(2α+β)y2+4αy=2(2+α)x2 ⇒β=0 for this to be circle (2+α)2x2+αy2+2x−4αy=0 
i.e. 2x2+2y2+2x−8y=0x2+y2+x−4y=0rd=41+4=217
Suppose the solution of the differential equation dxdy=βx−2αy−(βγ−4α)(2+α)x−βy+2 represents a circle passing through origin. Then the radius of this circle is :
Held on 6 Apr 2024 · Verified 6 Jul 2026.
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