Find-the-shortest-distance-from-the-origin-to-the-curve-xy-3-

Question Number 28198 by NECx last updated on 21/Jan/18

F i n d t h e s h o r t e s t d i s t a n c e f r o m

t h e o r i g i n t o t h e c u r v e x y = 3

Answered by mrW2 last updated on 22/Jan/18

d i s t a n c e o f p o i n t (x, y) t o t h e o r i g i n i s r .

r^{2} = x^{2} + y^{2}

x y = 3

\Rightarrow r^{2} = x^{2} + \frac{9}{x^{2}} ⩾ 2 \sqrt{x^{2} \times \frac{9}{x^{2}}} = 6 (A M ⩾ G M)

\Rightarrow r_{m i n} = \sqrt{6}

Commented by math solver last updated on 22/Jan/18

n i c e!