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Find the minimum distance between the curves y^2 = x-1 and x^2 = y-1                                   please give detail  solution

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7 years ago

147 Points
```										Dear Amrit pal

both curve are mirror image to each other about y=x
shortaset distance between these two corve is the segment made by line AB which is perpendicular to both the curve at point A and B respectively
as well as line AB is perpendicular to line y=x ,
i.e  slope of line AB is -1
let a general point A is(t2 ,t22 +1)  and point B is (t12 +1 ,t1)
slope of curve x2 =y-1 at A is  dy/dx = 2x
so slope for perpendicular at point A is -1/2x =-1/2t2
it will be equal to -1
-1/2t2 =-1
t2 =1/2

somilerly slope of perpendiculat on y2 =x-1 at point B is  = -2t1
-2t1 = -1
t1=1/2

so poins A and B become ( 1/2 ,5/4) and B is (5/4,1/2)
now find the distance between these two point.
So the minimum distance is (3/4) *√ 2

Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed  solution very  quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin

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7 years ago
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