(d) Equation of parabola whose axis is parallel to X axis and latus rectum is 4a (y−k)2 = 4a (x-h) (where h & k are arbitrary constants) differentiating b/s, we get 2 ( y - k )y' = 4ax ........(i) again differentiating b/s, we get. (y - k) y" + y’2 = 2a ⇒
2ax
y′
⋅y′′+y′2=2a from (i) ⇒ 2axy" + y' = 2ay’ ⇒ order 2