Answer :

Solution :

N : y = mx – 2am – am3

N : y = mx – 2m – m3

It passes through (2, 8)

8 = 2m – 2m – m3

⇒ m = – 2

∴  N : y + 2x = 12

Point of intersection of normal with y2 = 4x is (4, 4)

∴ Shortest distance =

$\sqrt{(4-<!--\; -\; -->2{)}^2+(4-<!--\; -\; -->8{)}^2}-<!--\; -\; -->\sqrt{4+64-<!--\; -\; -->64}$

$=\sqrt{20}-<!--\; -\; -->2$

$=2\sqrt{5}-<!--\; -\; -->2$