Question

On the parabola $y=x^2,$ the point at a least distance 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 $y=x^2$ ...(1)

Straight line $y=2x-4$ ....(2)

From (1) and (2), $x^2-2x+4=0$

Let $f\left(x\right)=x^2-2x+4$

$\therefore f^{\prime }\left(x\right)=2x-2$

For least distance, $f^{\prime }\left(x\right)=0\Rightarrow 2x-2=0\Rightarrow x=1$

From $y=x^2,y=1$

So the point least distance from the line is $(1,1)$.