Question

The degree of the differential equation obtained from the equation \((y-a)^2 = 4(x-b)\) [where \(a\) and b are arbitrary constants] is

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. not defined

Hint:

Eliminate both constants by differentiating twice.

Answer 1

The Correct Option is A

Step 1: Count the constants:
Two constants $a, b$ give a second-order equation.

Step 2: Eliminate:
From $(y-a)^2 = 4(x-b)$: $2(y-a)y_1 = 4$. Differentiating again: $2y_1^2 + 2(y-a)y_2 = 0$. Using $y - a = 2/y_1$: $y_1^3 + 2y_2 = 0$.

Step 3: Degree:
The highest derivative $y_2$ occurs with power 1 in a polynomial equation, so degree is 1, option (A).

Final Answer:
The degree is 1. \[ \boxed{\text{(A) }1} \]