Find the differential equation of the family of circles whose centres lie on `X`-axis.

Options

A. `(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0`
B. `y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) - 1 = 0`
C. `y""(d^(2)y)/(dx^(2)) - ((dy)/(dx))^(2) - 1 = 0`
D. `y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0`

Answer

D

Explanation

The equation of family of circle having centre at x-axis is `x^(2) + y^(2) - 2ax = 0`
On differentiating , we get
`2x + 2y""(dy)/(dx) - 2a = 0`
Again , differentiating , we get
`2 + 2 [y ""(d^(2) y)/(dx^2) + ((dy)/(dx))^(2)]`= 0
`iimplies y""(d^(2)y)/(dx^(2)) + ((dy)/(dx))^(2) + 1 = 0`