Question

diffrential equation for circle​

Answer 1

Answer:

Let the the circle be of radius r. Then,

(x−rcosθ)2+(y−rsinθ)2=r2(1)

2(x−rcosθ)+2(y−rsinθ)y′=0(2)

2x−2rcosθ+2yy′−2rsinθy′=0

1+yy′′+(y′)2−rsinθy′′=0

rsinθ=1+yy′′+(y′)2y′′(3)

Substitute (3) in (1),

(x−rcosθ)2+(y−rsinθ)2=r2

x2−2rxcosθ+y2−2rysinθ+r2sin2θ=r2sin2θ

x2−2rxcosθ+y2−2rysinθ=0

rcosθ=x2+y2−2rysinθ2x(4)

Now substitute (3) in (4) and then (3) and (4) in (2).

It is likely that there may be an easier way than this.

Step-by-step explanation:

hope it help u

Answer 2

Answer:

Let the the circle be of radius r. Then,

(x−rcosθ)2+(y−rsinθ)2=r2(1)

2(x−rcosθ)+2(y−rsinθ)y′=0(2)

2x−2rcosθ+2yy′−2rsinθy′=0

1+yy′′+(y′)2−rsinθy′′=0

rsinθ=1+yy′′+(y′)2y′′(3)

Substitute (3) in (1),

(x−rcosθ)2+(y−rsinθ)2=r2

x2−2rxcosθ+y2−2rysinθ+r2sin2θ=r2sin2θ

x2−2rxcosθ+y2−2rysinθ=0

rcosθ=x2+y2−2rysinθ2x(4)

Now substitute (3) in (4) and then (3) and (4) in (2).

It is likely that there may be an easier way than this.

Step-by-step explanation:

hope it help u