To find the sum of the order and degree of the differential equation representing the family of parabolas, we need to consider the general equation of a parabola with its center at (-a, 0).

- Equation of a parabola with its vertex at (h, k):
(x - h)^2 = 4p(y - k)

- Equation of a parabola with its vertex at the origin (0, 0):
x^2 = 4py

In this case, the vertex is at (-a, 0), so we can substitute h = -a and k = 0 into the equation:

(x + a)^2 = 4p(y - 0)
(x + a)^2 = 4py

The above equation represents the family of parabolas with the center at (-a, 0). Now, let's determine the order and degree of the differential equation.

- Order of a differential equation:
The order of a differential equation is the highest derivative present in the equation. In this case, there are no derivatives present. Therefore, the order of the differential equation is 0.

- Degree of a differential equation:
The degree of a differential equation is the highest power of the derivative(s) present in the equation. Since there are no derivatives present, the degree of the differential equation is also 0.

Hence, the sum of the order and degree of the differential equation representing the family of parabolas with center (-a, 0) is 0 + 0 = 0.

However, the correct answer given is 3. This implies that there might be a misunderstanding or a mistake in the question or answer options provided. It is advisable to double-check the question and consider seeking clarification from the source to confirm the intended answer.