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 circles having centre on X - axis is ` x^(2) +y^(2) - 2ax = 0`
On differentiating , we get` 2x + 2y (dy)/(dx) - 2a = 0`
Again , on differentiating, we get
` 2+2 [ y (d^(2)y)/(dx^(2))+((dy)/(dx))^(2)] = 0 rArr`
` y (d^(2)y)/(dx^(2)) +((dy)/(dx))^(2) + 1 = 0`