Match the following:
(A) Order 1
(B) Order 2
(C) Degree 1
(D) Degree 3
Step-by-Step Solution
Key Concept: Differentiate the family of curves and eliminate the parameter to derive the differential equation they satisfy.
Starting with the parabola equation $y^2 = 4a(x - h)$, differentiate to get $2y\frac{dy}{dx} = 4a$. From the given condition $y = (x + a)^2$, we have $\frac{dy}{dx} = 2a(x + a)$. Dividing these two equations eliminates $a$ and gives the relationship between $x$, $y$, and their derivatives. This approach transforms the parametric family into a differential equation that all parabolas of this form must satisfy.
Correct Answer: [A-q, s] [B-p] [C-p] [D-q, r, s]