The solution of the differential equation `(dy)/(dx)=(a x+g)/(b y+f)` represents a circle when `a=b` b. `a=-b` c. `a=-2b` d. `a=2b`

Options

A. a=b
B. `a=-b`
C. `a=-2b`
D. `a=2b`

Answer

b

Explanation

We have ,
` (dy)/(dx) = (ax +g)/(by+f)`
` rArr (by + f) dy = (ax + g ) dx`
Onintegrating ,we get
` (by^(2))/2 +fy = (ax^(2))/2 + gx + C`
`rArr ax^(2) - by^(2) + 2gx - 2fy +C = 0`
This represents a circle , if a = -b