Find the differential equation from the equation `(x-h)^(2)+(y-k)^(2)=a^(2)` by eliminating `h` and `k`.

Explanation

`(x-h)^(2)+(y-k)^(2)=a^(2)`………..`(1)`
`implies 2(x-h)+2(y-k)(dy)/(dx)=0`
`implies(x-h)=-(y-k)*(dy)/(dx)`
`implies1=-[(y-k)*(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)]`
`implies y-k=-(1+((dy)/(dx))^(2))/((d^(2)y)/(dx^(2)))`
`(x-h)=(1+((dy)/(dx))^(2))/((d^(2)y)/(dx^(2)))*(dy)/(dx)`
From eq. `(1)`
`([1+((dy)/(dx))^(2)]^(2))/(((d^(2)y)/(dx^(2)))^(2))((dy)/(dx))^(2)+([1+((dy)/(dx^(2)))])/(((d^(2)y)/(dx^(2)))^(2))=a^(2)`
`implies[1+((dy)/(dx))^(2)]^(2)*[((dy)/(dx))^(2)+1]=a^(2)*((d^(2)x)/(dx))^(2)`
`implies[1+((dy)/(dx))^(2)]^(3)=a^(2)*((d^(2)x)/(dx))^(2)`