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BITSAT2017MathematicsApplication of DerivativesActual

The shortest distance between the parabolas y 2 = 4 x and y 2 = 2 x - 6 is

Options

  1. A2
  2. B5
  3. C3
  4. DNone

Correct answer

B. 5

Step-by-step solution

Shortest distance between two curves occured along the common normal. ∴ Normal to y 2 = 4 x at m 2 , 2 m is y + m x - 2 m - m 3 = 0 Normal to y 2 = 2 x - 3 at m 2 2 + 3 , m is y + m x - 3 - m - m 3 2 = 0 Both normals are same, if - 2 m - m 3 = - 4 m - 1 2 m 3 ⇒ m = 0 , 2 So, points will be ( 4 , 4 ) and ( 5 , 2 ) or ( 4 , - 4 ) and ( 5 , - 2 ) . Hence, shortest distance will be ( 1 + 4 ) = 5 unit.

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