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-

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