MHT CET 2017 Math Solved Paper

(a) Let vertex of parabola be (0, k) as axis of parabola is Y-axis
So, equation of parabola is
(x−0)2 = 4 a (y -k )
⇒ x2 = 4ay - 4ak

After, differentiating both sides w.r.t, ‘x’, we get
2x = 4a

dy

dx

Therefore,

1

2a

=

1

x

dy

dx

Again differentiating on both sides w.r.t. ‘x’, we get

d

dx

(

1

x

,

dy

dx

) =

d

dx

(

1

2a

)
⇒

1

x

⋅

d2y

dx2

+

dy

dx

(−

1

x2

)=0
Hence, x

d2y

dx2

−

dy

dx

= 0