Find the minimum distance between the curves y^2 = x-1 and x^2 = y-1 please give detail solution
Interesting problem.
I found the distance is from point ( 5/4 , 1/2 ) to point ( 1/2, 5/4 )
Note the symmetry of the curve.
So the minimum distance is (3/4) * sqrt (2 ) which is approximately 1.06
I will come back with more details.
My general approach is this:
let the points be (x1,y1) and (x2,y2 )
Find the distance square
d^2 = (x1 -x2) ^2 + (y1 -y2)^2
eliminate (y1, y2 ) from d^2
set ( d (d^2) / dx1 =0 , d (d^2) /dx2 =0 )
solve for (x1,x2)
--
regards
Ran\mesh
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