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

Answer: (A)

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