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Question

If the line x+y=1 touches the parabola y2y+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=1y (1)
Given equation of parabola is
y2y+x=0
y2y+1y=0 (Using (1))
(y1)2=0
y=1
So, x=0
Hence, the point of contact is (0,1)

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