Mathematics

The shortest distance between the line $y=x$ and the curve $y^2=x-2$ is :

$\dfrac{7}{4\sqrt{2}}$

SOLUTION
we have ,$2y.\dfrac{dy}{dx}=1\Rightarrow\dfrac{dy}{dx}]_{P(2+t^2,t)}=\dfrac{1}{2t}=1$
$\Rightarrow t=\dfrac{1}{2}$
$\therefore P\left(\dfrac{9}{4},\dfrac{1}{2}\right)$
So, shortest distance
$=\dfrac{\left|\dfrac{9}{4}-\dfrac{2}{4}\right|}{\sqrt{2}}=\dfrac{7}{4\sqrt{2}}$

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Single Correct Medium Published on 09th 09, 2020
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