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Find the minimum distance between the curves y^2 = x-1 and x^2 = y-1 please give detail solution
Both the parabolas are symmetric to the line x=y.
Therefore, equating their slopes to 1,
for parabola x^2=y-1,
dy/dx = 1
2x =1
x=1/2
corresponding value of y by putting the value of x in the eq. of parabola we get y=5/4
Similarly, for the parabola y^=x-1,
dx/dy =1
2y=1
y=1
corresponding value of x by putting the value of y in the eq. of parabola we get x=5/4
The minimum distance is between the points (1/2,5/4) and (5/4,1/2)
And 3√2/4
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