By Variable separable,

⇒ (by + f) dy = (ax + g) dx

Integrating both sides

⇒ ∫ (by + f) dy = ∫ (ax + g) dx

⇒ by² + 2fy = ax² + 2gx + C^’

Where C’ = 2C

We know general solution of circle is

(x – h)² + (y – k)² = r²

Where (h, k) is center of the circle and r is radius.

By completing square method

Now to form above equation as equation of circle we need

i.e. a = -b

= (B)