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The shortest distance between the line x...

The shortest distance between the line x=y and the curve `y^(2)=x-2` is

A

`11/(4sqrt(2))`

B

`7/8`

C

`7/(4sqrt(2))`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
`y^2=x-2, " "y =x`
`y^2=(x-2)," " y^2=4xx1/4(x-2)`
vertex =(2.0), `a=1/4`
tangent of slpoe 1 on parabola
`y=1xx(x-2)+1/4, " " y=x-7/4`
Distance of this line from y=x
`d=7/(4xxsqrt1+1)=7/(4sqrt2)`
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