Question

The differential equation whose solution is (x – h)² + (y – k)² = a² is (where a is a constant) ______.

Options

• `[1 + (dy/dx)^2]^3 = a^2((d^2y)/(dx^2))^2`

• `[1 + (dy/dx)^2]^3 = a^2(d^2y)/(dx^2)`

• `[1 + (dy/dx)]^3 = a^2((d^2y)/(dx^2))^2`

• `[1 + (dy/dx)]^3 = a^2(d^2y)/(dx^2)`

Answer 1

The differential equation whose solution is (x – h)² + (y – k)² = a² is (where a is a constant) `underlinebb([1 + (dy/dx)^2]^3 = a^2((d^2y)/(dx^2))^2)`.

Explanation:

(x – h)² + (y – k)² = a²  ...(1)

⇒ `2(x - h) + 2(y - k) (dy)/(dx)` = 0

⇒ `(x - h) + (y - k) (dy)/(dx)` = 0  ...(2)

⇒ `1 + (dy/dx)^2 + (y - k) (d^2y)/(dx^2)` = 0  ...(3)

From (1), (2) and (3) we get

`[1 + (dy/dx)^2]^3 = a^2((d^2y)/(dx^2))^2`