A-circle-tangents-to-x-and-y-axes-and-x-1-2-y-1-2-a-1-2-find-its-radious-

Question Number 58282 by behi83417@gmail.com last updated on 20/Apr/19

A circle tangents to : x and y axes and

x^{\frac{1}{2}} + y^{\frac{1}{2}} = a^{\frac{1}{2}} . find its radious .

Answered by mr W last updated on 21/Apr/19

d u e t o s y m m e t r y t h e c i r c l e t o u c h e s

t h e c u r v e a t (t, t) .

\sqrt{t} + \sqrt{t} = \sqrt{a}

\Rightarrow t = \frac{a}{4}

e q n . o f c i r c l e : {(x - r)}^{2} + {(y - r)}^{2} = r^{2}

{(t - r)}^{2} + {(t - r)}^{2} = r^{2}

\sqrt{2} (t - r) = \pm r

\Rightarrow r = \frac{\sqrt{2}}{\sqrt{2} + 1} t = (2 - \sqrt{2}) t = \frac{2 - \sqrt{2}}{4} a

o r

\Rightarrow r = \frac{\sqrt{2}}{\sqrt{2} - 1} t = (2 + \sqrt{2}) t = \frac{2 + \sqrt{2}}{4} a

(b u t t h i s c i r c l e i n t e r s e c t s a l s o w i t h

t h e c u r v e .)

Commented by behi83417@gmail.com last updated on 21/Apr/19

t h a n k s a l o t d e a r m a s t e r .

i h a v e s o m e p r o b l e m w i t h l a s t l i n e!

Commented by mr W last updated on 21/Apr/19

t h e c i r c l e w i t h r = \frac{2 - \sqrt{2}}{4} a o n l y t a n g e n t s

t h e c u r v e, b u t t h e c i r c l e w i t h r = \frac{2 + \sqrt{2}}{4} a

n o t o n l y t a n g e n t s t h e c u r v e b u t a l s o

i n t e r s e c t s w i t h i t .

Commented by mr W last updated on 21/Apr/19

Commented by behi83417@gmail.com last updated on 21/Apr/19

t h a n k y o u s o m u c h m a s t e r .

p e r f e c t! n o w i t i s c l e a r t o m e .