AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

The equation of family of parabolas with focus and the x axis is,
y2=4a(x−a)
Differentiate with respect to x
2y‌

dy

dx

‌‌=4a
a‌‌=‌

y

2

‌

dy

dx

Therefore,

y2=2y‌

dy

dx

(x−‌

y

2

)‌

dy

dx

y2‌‌=y‌

dy

dx

(2x−y)‌

dy

dx

y(‌

dy

dx

)2−2x(‌

dy

dx

)+y‌‌=0
Hence, the order of the differential equation is 1