Question 203944
The  equation  of  a  circle  is  x^2 +y^2 =r^2,,,,in  this  case  x^2+y^2=2,,,
or  r=sqrt2
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The  tan  line  has  the  eqn,,,,y=mx+3,,,,with  std  eqn,,y=mx=b,,,,b=3
or  the  y  intercept  is  at  (0,3)
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Drawing  a  rough  sketch  helps.  Circle  about  origin  with  r= sqrt2 = 1.414
tan  line thru  (0,3) to  either  side  of  circle.
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Remember  that  a  line  tan  to a  circle,  touches  only  one  point,  perpendicular  to  the  radius.
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Adding  such  a  line  to  the  sketch,  finds  a  rt triangle, one  vertex  at (0,0),  another  at (0,3) .
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Legs  of  this  triangle  are  3  and  sqrt2.
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let  angle  formed  by  vertical  axis and  tan  line be  "a".
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sin a = sqrt2 /3 = .4714,,,,,a=28.1255 degrees
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tan  a = x/y  of  line  tan  to  circle,,,or  y/x= 1/tan a=1/tan 28.1255= 1.87
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but  m=y/x =1.87,,,,this  is  negative  on  rt  side  of  circle  and  positive  on left  side.
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from,,y=mx +b,  lt  side ln  is  y=1.87x +3,,rt side ln is  y= -1.87x +3
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