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

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

Grade:12

2 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

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

vikas askiitian expert
509 Points
10 years ago

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

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