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Prove that the straight line x+y=1 touches the parabola y= x-x^2

Prove that the straight line x+y=1 touches the parabola y= x-x^2

Grade:11

1 Answers

Arun
25763 Points
4 years ago
If line cuts the parabola then there will be two points
& if line touches the parabola then there will be only one
point.
Now,
Put y= 1-x in the equation of parabola
1-x = x- x^2
x^2 -2 x+ 1= 0
when solving quadratic
(x-1)^2 = 0
x = 1
Hence y= 0
As we see that there is only one solution
So this will be a tangent to parabola at (1, 0)

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