Question 194672
4x^2 -y^2 +1 =0
,
rearranging
,
x^2/(1/4) -y^2/1 = -1
,
multiply  by  (-1)
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- x^2/(1/4)  +y^2/1 = 1
,
this  fits  form  of a  (y) hyperbola,,,,  with  a^2 =1/4,,,,b^2 = 1
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remember  c^2 = a^2  + b^2  = 1/4 +1 = 1.25
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c  = 1.118
,
FOCI  ( 0,  +/- 1.118)  or   (0,1.118) and  (0, -1.118)