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  • If the line touches the parabola  <img alt="\mathrm{y^{2}-y+x=0}" src="https:

If the line \mathrm{x+y=1} touches the parabola  \mathrm{y^{2}-y+x=0}, then the co-ordinates of the point of contact are

Option: 1

(1,1)


Option: 2

\left(\frac{1}{2}, \frac{1}{2}\right)


Option: 3

(0,1)


Option: 4

(1,0)


Answers (1)

best_answer

The tangent at \left(x_{1}, y_{1}\right) is \mathrm{2 y_{1}-y-y_{1}+x+x_{1}=0} comparing it with  \mathrm{x+y-1= 0 }, we get \left(\mathrm{x}_{1}, \mathrm{y}_{1}\right) \equiv(0,1).

Hence (C) is the correct answer.

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