Step 1 :The equation given is of the form of a general circle equation, which is \((x-h)^2 + (y-k)^2 = r^2\), where (h,k) is the center of the circle and r is the radius.
Step 2 :However, the equation given can also represent an ellipse, parabola, or hyperbola depending on the values of a, b, and c.
Step 3 :Therefore, we cannot say that every equation of the given form will always represent a circle.
Step 4 :Final Answer: \(\boxed{\text{False}}\)