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

A circle tangents to :x and y axes and      x^(1/2) +y^(1/2) =a^(1/2) .find its radious.

Acircletangentsto:xandyaxesandx12+y12=a12.finditsradious.

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

due to symmetry the circle touches  the curve at (t,t).  (√t)+(√t)=(√a)  ⇒t=(a/4)  eqn. of circle: (x−r)^2 +(y−r)^2 =r^2   (t−r)^2 +(t−r)^2 =r^2   (√2)(t−r)=±r  ⇒r=((√2)/((√2)+1))t=(2−(√2))t=((2−(√2))/4)a  or  ⇒r=((√2)/((√2)−1))t=(2+(√2))t=((2+(√2))/4)a  (but this circle intersects also with  the curve.)

duetosymmetrythecircletouchesthecurveat(t,t).t+t=at=a4eqn.ofcircle:(xr)2+(yr)2=r2(tr)2+(tr)2=r22(tr)=±rr=22+1t=(22)t=224aorr=221t=(2+2)t=2+24a(butthiscircleintersectsalsowiththecurve.)

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

thanks a lot dear master.  i have some problem with last line!

thanksalotdearmaster.ihavesomeproblemwithlastline!

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

the circle with r=((2−(√2))/4)a only tangents  the curve, but the circle with r=((2+(√2))/4)a  not only tangents the curve but also  intersects with it.

thecirclewithr=224aonlytangentsthecurve,butthecirclewithr=2+24anotonlytangentsthecurvebutalsointersectswithit.

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

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

thank you so much master.  perfect!now it is clear to me.

thankyousomuchmaster.perfect!nowitiscleartome.

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