Question

Differential equation of all circles of radius r is of

• A. third order second degree
• B. second order second degree
• C. second order third degree
• D. none of these

Answer 1

The correct option is D none of these

$(x-h{)}^2+(y-k{)}^2=r^2$ (r= constant)

Differentiating w.r.t x, we get

$2(x-h)+2(y-k)\frac{dy}{dx}=0$ ....(1)

Again differentiating w.r.t x and using (2), we get)

$1+(y-k)\frac{d^{2}y}{d{x}^2}+{\left(\frac{dy}{dx}\right)}^2=0$

So, order is $2$ and degree is $1.$