The order and degree of differential equation of family of circles touching y axis at origin, is

Question

The order and degree of differential equation of family of circles touching y axis at origin, is (A) 1,1 (B) 1,2 (C) 2,1 (D) 2,2

Tardigrade Admin · Accepted Answer

(x-α)2+(y-0)2=α2 x2+y2-2 α x=0 ....(i) 2 x+2 y (d y/d x)-2 α=0 α=x+y (d y/d x) .....(ii) equation of differential equation x2+y2=2 x(x+y (d y/d x)) order =1 degree =1

Q. The order and degree of differential equation of family of circles touching $y$ axis at origin, is

1,1

1,2

2,1

2,2

$(x - α)^{2} + (y - 0)^{2} = α^{2}$
$x^{2} + y^{2} - 2 αx = 0....$ (i)
$2 x + 2 y \frac{d y}{d x} - 2 α = 0$
$α = x + y \frac{d y}{d x} .....$ (ii)
equation of differential equation
$x^{2} + y^{2} = 2 x (x + y \frac{d y}{d x})$
order $= 1$
degree $= 1$

Q. The order and degree of differential equation of family of circles touching y axis at origin, is

1,1

1,2

2,1

2,2

(x−α)2+(y−0)2=α2 x2+y2−2αx=0....(i) 2x+2ydxdy​−2α=0 α=x+ydxdy​.....(ii) equation of differential equation x2+y2=2x(x+ydxdy​) order =1 degree =1

Q. The order and degree of differential equation of family of circles touching $y$ axis at origin, is

$(x - α)^{2} + (y - 0)^{2} = α^{2}$
$x^{2} + y^{2} - 2 αx = 0....$ (i)
$2 x + 2 y \frac{d y}{d x} - 2 α = 0$
$α = x + y \frac{d y}{d x} .....$ (ii)
equation of differential equation
$x^{2} + y^{2} = 2 x (x + y \frac{d y}{d x})$
order $= 1$
degree $= 1$