Question

On the parabola $y=x^2$, the point least distant from the straight line $y=2x-4$ is

• A. $(1,1)$
• B. $(1,0)$
• C. $(1,-1)$
• D. $(0,0)$

Answer 1

The correct option is A $(1,1)$

Given, parabola is $y=x^2$ ....(i)
and straight line is $y=2x-4$ ....(ii)
From equations (i) and (ii), we get
$x^2-2x-4=0$
Let $f\left(x\right)=x^2-2x-4$
Thus $f^{{}^{\prime }}\left(x\right)=2x-2$
For least distance, put $f^{{}^{\prime }}\left(x\right)=0$
$\Rightarrow 2x-2=0$
$\Rightarrow x=1$
From equation (i), we have $y=1$
Hence, the point least distant from the line is $(1,1)$.