Minimum distance between the curves `y^2=4x and x^2+y^2-12x+31=0` is

Explanation

`(beta^2/4,beta)` point on the padoda

`2*(dy)/(dx)*y=4`

`(dy)/(dx)=2/y=2/beta`

`(beta-0)/((beta^2/4)-6)*2/beta=-1`

`8/(beta^2-24)=-1`

`sqrt((beta^2/4-6)^2+beta^2)-sqrt5`

`sqrt((16/4-6)^2+16)-sqrt5`

`sqrt(4+16)-sqrt5=2sqrt5-sqrt5=sqrt5`

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