Question

The differential equation of all circles of radius a is of order

• A. 2
• B. 3
• C. 4
• D. none of these

Hint:

To obtain the differential equation of a circle, differentiate its equation twice.

Answer 1

The Correct Option is B

Step 1: Equation of a circle.
The general equation of a circle with center (h, k) and radius a is:
(x − h)² + (y − k)² = a²

Step 2: Differentiating the equation.
To find the differential equation, we differentiate the equation of the circle twice. The first differentiation gives the first-order equation, and the second differentiation gives the second-order equation.

d/dx [(x − h)² + (y − k)²] = d/dx [a²]

The second differentiation will yield a third-order differential equation. Therefore, the order of the differential equation is 3.

Step 3: Conclusion.
Thus, the differential equation of all circles of radius a is of order 3.

Final Answer: 3.