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The differential equation whose solution is `(x-h)^2+ (y-k)^2=a^2` is (a is a constant)A. order is 2B. order is 3C. degree is 2D. degree is 3 |
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Answer» Correct Answer - A::C We have `(x-h)^(2)+(y-k)^(2)=a^(2)`…………..(1) Differentiating w.r.t. x, we get `2(x-h)+2(y-k)(dy)/(dx)=0` or `(x-h)+(y-k)(dy)/(dx)=0`……….(2) Differentiating w.r.t. x, we get `1+((dy)/(dx))^(2)+(y-k)(d^(2)y)/(dx^(2))=0` ………..(3) From equation (3), `y-k=-(1+p^(2))/q`, where `p=(dy)/(dx), q=(d^(2)y)/(dx^(2))` Putting the value of `y-k` in equation (2), we get `x-h=(1+p^(2))=a^(2)` or `[1+((dy)/(dx))^(2)]^(3)=a^(2)(d^(2)y)/(dx^(2))^(2)` Which is the required differential equation. |
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