If the line x+y=1 touches the parabola y2−y+x=0, then the coordinates of the point of contact are
A
(1,1)
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B
(12,12)
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C
(0,1)
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D
(1,0)
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Solution
The correct option is C(0,1) Given equation of line is x+y=1 x=1−y⋯(1)
Given equation of parabola is y2−y+x=0 ⇒y2−y+1−y=0⋯(Using (1)) ⇒(y−1)2=0 ⇒y=1
So, x=0
Hence, the point of contact is (0,1)