Question

The shortest distance between the line x – y + 1 = 0 and the curve x = y² is .........

(a) [(3√2)/5]

(b) [(2√3)/8] 

(c) [(3√2)/8]

(d) [(2√2)/5]

Answer 1

The correct option (c) [(3√2)/8]   

Explanation:

line: x – y + 1 = 0 &  slope is 1.

curve: x = y²  

∴ 1 = 2y ∙ (dy/dx)  

∴     (dy/dx) = (1/2y)  i.e. slope = (1/2y)

∴   (1/2y) = 1 ⇒ y = (1/2) and     x = (1/4)  

∴    (x, y) = [(1/4), (1/2)]

Shortest distance = [{|(1/4)(1) – (1/2)(1) + 1|}/√(1 + 1)]  = [3/(4√2)]  = [(3√2)/8].