AP EAMCET Engineering 2018 Apr 22 Shift 1 Paper

The equation of the family of parabolas with focus at the origin and x-axis as its axis is given by
y2=4a(x+a)
=4ax+4a2 ....(i)
Differentiate the above expression
2y

dy

dx

=4a
a=

1

2

y

dy

dx

....(ii)
From cxpression (i) and (ii)
y2=2xy

dy

dx

+y2(

dy

dx

)2
Here order =m=1 and =n=2
Now
mn−m+n=1×2−1+2
=3