What-are-the-coordinates-of-the-points-on-the-curve-x-2-y-2-16-which-nearest-to-0-6-

Question Number 157947 by cortano last updated on 30/Oct/21

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

p o i n t s o n t h e c u r v e x^{2} - y^{2} = 16

w h i c h n e a r e s t t o (0, 6) ?

Answered by mr W last updated on 30/Oct/21

d^{2} = x^{2} + {(y - 6)}^{2}

= 16 + y^{2} + {(y - 6)}^{2}

= 2 {(y - 3)}^{2} + 34 ⩾ 34

d ⩾ \sqrt{34} = n e a r e s t d i s t a n c e

a t y = 3, x = \pm \sqrt{16 + 3^{2}} = \pm 5

Commented by cortano last updated on 30/Oct/21

y e s

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