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