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

Options

A. order is 2
B. order is 3
C. degree is 2
D. degree is 3

Answer

A, C

Explanation

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.