Therefore, equation
of family P is
y2 = 4ax (1)
Differentiating both sides of equation (1) with respect to x, we get
2
dy
y dx  = 4a (2)
Substituting the value of 4a from equation (2)
in equation (1), we get
y2 =
2
( )
ydy
x
dx
⎛
⎞
⎜
⎟
⎝
⎠
or
2
2
dy
y
−xy dx
 = 0
which is the differential equation of the given family
of parabolas Fig 9