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The shortest distance between the point ...

The shortest distance between the point `(0, 1/2)` and the curve ` x = sqrt(y) , (y gt 0 ) ` , is:

A

`3/2`

B

`(sqrt5)/(2)`

C

`(sqrt3)/(2)`

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
`x = sqrt(y) , x^2 = y`
` y = (t^2)/(4) , x = t/2`
` (t/2 , (t^4)/(4) ) ` (shortest distance lies along common normal )
Equation of normal: ` x = - ty + 2at + at^3`
Slope ` = - 1/t`
` - 1/t = ((t^2)/(4) - 1/2)/(t/2 - 0) , t = 0 rArr x = 0 , y = 0 `
point (0,0) Distance ` = sqrt((0-0)^2 + ( 0 - 1/2)^2 ) = 1/2 `
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