SOLUTION: i keep coming up with the wrong answers for the foci of this equation. please help. 4x^2-y^2+1=0

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Question 194672This question is from textbook
: i keep coming up with the wrong answers for the foci of this equation. please help.
4x^2-y^2+1=0 This question is from textbook

Found 2 solutions by RAY100, solver91311:
Answer by RAY100(1637) (Show Source):
You can put this solution on YOUR website!
4x^2 -y^2 +1 =0
,
rearranging
,
x^2/(1/4) -y^2/1 = -1
,
multiply by (-1)
,
- x^2/(1/4) +y^2/1 = 1
,
this fits form of a (y) hyperbola,,,, with a^2 =1/4,,,,b^2 = 1
,
remember c^2 = a^2 + b^2 = 1/4 +1 = 1.25
,
c = 1.118
,
FOCI ( 0, +/- 1.118) or (0,1.118) and (0, -1.118)

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

First, put it in standard form. Either:

or

If you add -1 to both sides you have something equal to -1 so you have to multiply the whole thing by -1, that gives you:

This hyperbola is centered at the origin and, because the y-term is the positive term, it opens up and down and the foci are on the y-axis at (0,c) where

Hence, the foci are at and

John