The differential equation whose solution is (x-h)²+(y-k)²=a²(a is a constant ) , is

Step-by-step solution

Given, (x-h)²+(y-k)²=a² ...(i) array lr & 2(x-h)+2(y-k) d y d x =0 & (x-h)+(y-k) d y d x =0 array Again differentiating (y-k)=- 1+ ( d y d x )² d² y / d x² Putting in Eq. (ii), we get array l x-h=-(y-k) d y d x = [1+ ( d y d x )² ] d y d x d² y d x² array Putting in Eq. (i), we get array l [1+ ( d y d x )² ]² ( d y d x )² ( d² y d x² )² [1+ ( d y d x )² ]² [ ( d y d x )²+1 ]=a² ( d² y d x² )² + [1+ ( d y d x )² ]² ( d² y d x² )² =a² [1+ ( d y d x )² ]³=a² ( d² y d x² )² array