if x+y=k touches the parabola y=x-x² then k=?

Dear Nikhil, 

y=k-x=x-x², x²-2x+k=0,x=1±√(1-k), y=x-x², dy/dx=1-2x= -1±√(1-k)=-1 because slope of x+y=k=-1, therefore,k=1

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Chetan Mandayam Nayakar – IIT Madras

x+y=k............1

y=x-x² ...............2

from 1 and 2

k-x=x-x²

x² -2x+k=0 .............3

if line touches the parabola then there will be only one point of contact of line with parabola..

for this condition ,in eq 3 there should be only one value of x

so discriminant =0

   b² =4ac

  4k=4

   k=1