The shortest distance between the line y - x = 1 and curve

The shortest distance between the line y - x = 1 and curve y = x2 is

  1. √3/4
  2. 4/√3
  3. 8/3√2
  4. 3√2/8

Answer

y - x =1

y = x2

2y dy/dx = 1

dy/dx = 1/2y = 1

y = 1/2, x = 1/4

Tangent at (1/4,1/2)

1/2y = 1/2(x + 1/4)

y - x = 1/4

The correct option is D.