Question

On the parabola $y=x^2$, the point 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)

$\text{Given, parabola}y=x^2.....\left(i\right)\text{Straight line}y=2x-4.....\left(ii\right)From\left(i\right)and\left(ii\right),x^2-2x+4=0Letf\left(x\right)=x^2-2x+4,\therefore f^{\prime }\left(x\right)=2x-2.\text{For least distance},f^{\prime }\left(x\right)=0\Rightarrow 2x-2=0\Rightarrow x=1Fromy=x^2,y=1\text{So the point least distant from the line is}(1,1).$