What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?

Step-by-step solution

General equation of circle, [x-h]^2+(y-k)^2=r^2 As the circle touches both the coordinate axes in first quadrant, aligned & Centre, c(h, k)=(r, r) & (x-r)^2+(y-r)^2=r^2 ... (i) & x^2-2 x r+y^2-2 y r+r^2=0 & 2 x-2 r+2 y y₁-2 r y₁=0 & r (1+y₁ )=x+y y₁ & r= x+y y₁ 1+y₁ aligned Substituting the value of r in eqn.(1) and solving that eqn. we finally get. (x+y y₁ )^2=(x-y)^2 (1+y₁^2 ) Max power of y₁= Degree =2