Question

If the line $x+y=1$ touches the parabola $y^2-y+x=0$, then the coordinates of the point of contact are

• A. $(1,1)$
• B. $(\frac{1}{2},\frac{1}{2})$
• C. $(0,1)$
• D. $(1,0)$

Answer 1

The correct option is C $(0,1)$

Given equation of line is
$x+y=1$
$x=1-y\cdots \left(1\right)$
Given equation of parabola is
$y^2-y+x=0$
$\Rightarrow y^2-y+1-y=0\cdots (\text{Using (1))}$
$\Rightarrow (y-1{)}^2=0$
$\Rightarrow y=1$
So, $x=0$
Hence, the point of contact is $(0,1)$