If the solution of the differential equation
`(dy)/(dx)=(ax+3)/(2y+f)`
represents a circle, then the value of 'a' is

Options

A. 2
B. -2
C. 3
D. -4

Answer

b

Explanation

We have , ` (dy)/(dx) = (ax+3)/(ay+f)rArr (ax+3) dx = (2y +f)dy`
On integrating , we obtain
` a*(x^(2))/2 + 3x = y^(2) +fy +C`
` :. -a/2 x^(2) +y^(2) - 3x +fy +C = 0 `
This will represent a circle , if `-a/2 =1`
` [ :' "coefficient of " x^(2) = "coefficient of " y^(2)]`
and ` 9/4 +(f^(2))/4 -c gt0 [ "using" g^(2)+f^(2) -c gt 0]`
` :. a = -2 and 9 + f^(2) - 4 c gt 0`