find the value of [v] if v denotes maximum value of x^2 + y^2 , where (x+5)^2 + (y−12)^2 = 14 (hint [•] repersent greatest integer function of “ •”)


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Question Number 169382 by infinityaction last updated on 29/Apr/22

$find the value of [v] if v den o tes maximum$ $value of x^{2} + y^{2}, where {(x + 5)}^{2} + {(y - 12)}^{2} = 14$ $(hint [∙] repersent greatest integer function of ‘ ‘ ∙^{″})$
Commented by infinityaction last updated on 29/Apr/22

$t h a n k y o u s i r a n d$ $g o t m y m i s t a k e$
Commented by infinityaction last updated on 29/Apr/22

$s i r s o l u t i o n$
Commented by mr W last updated on 29/Apr/22

$v = x^{2} + y^{2} = r^{2}$ $r i s t h e d i s t a n c e f r o m t h e o r i g i n t o$ $a p o i n t o n t h e c i r c l e$ ${(x + 5)}^{2} + {(y - 12)}^{2} = 14 .$ ${i t}^{'} s c l e a r t h a t t h e m a x i m u m d i s t a n c e$ $i s t h e d i s t a n c e f r o m$ $(0, 0) t o (- 5, 12) p l u s t h e r a d i u s o f$ $t h e c i r c l e, w h i c h i s \sqrt{14} . i . e .$ $r_{m a x} = \sqrt{{(- 5 - 0)}^{2} + {(12 - 0)}^{2}} + \sqrt{14} = 13 + \sqrt{14}$ $v = r_{m a x}^{2} = {(13 + \sqrt{14})}^{2} \approx 280.3$
Commented by greougoury555 last updated on 29/Apr/22

$\Rightarrow v = \sqrt{14} + \sqrt{{(- 5)}^{2} + 12^{2}} = 13 + \sqrt{14}$ $\Rightarrow [v] = 16$
Commented by infinityaction last updated on 29/Apr/22

$u s e c i r c l e e q u a t i o n$ $s a m e s o l u t i o n s i r$ $b t w t h a n k s$
Commented by infinityaction last updated on 29/Apr/22

$b u t s i r i a m c o n f u s e d$ $b e c a u s e l e t x = - 5 a n d y = \sqrt{14} + 12$ $t h e n x^{2} + y^{2} = 272.799$ $[x^{2} + y^{2}] = [272.799] = 272$
Commented by mr W last updated on 29/Apr/22

$v = {(13 + \sqrt{14})}^{2} \approx 280.3$ $[v] = 280$
	Answered by kapoorshah last updated on 29/Apr/22

	$l e t x + 5 = \sqrt{14} \cos α$ $y - 12 = \sqrt{14} \sin α$ $x^{2} + y^{2} = {(\sqrt{14} \cos α - 5)}^{2} + {(\sqrt{14} \sin α + 12)}^{2}$ $= 14 - 10 \sqrt{14} \cos α + 24 \sqrt{14} \sin α + 169$ $= 183 + 26 \sqrt{14} \cos (α - \tan^{- 1} (- \frac{12}{5}))$ $[v] = 183 + 26 \sqrt{14}$ $\approx 280, 283$
	Commented by infinityaction last updated on 29/Apr/22

	$t h a n k y o u$
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