SOLUTION: what is the foci and asymptotes of the hyperbola 4x^-y^2=1 with steps

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Question 890186: what is the foci and asymptotes of the hyperbola 4x^-y^2=1
with steps
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
what is the foci and asymptotes of the hyperbola 4x^2-y^2=1
with steps
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Given hyperbola has a horizontal transverse axis with center at the origin.
Its standard form of equation:
x%5E2%2Fa%5E2-y%5E2%2Fb%5E2=1
For given hyperbola:
center:(0,0)
4x^2-y^2=1
x^2/(1/4)-y^2=1
a^2=1/4
a=1/2
b^2=1
b=1
c^2=a^2+b^2=1/4+1=5/4
c=√5/2
foci: (0±c, 0)=0±√5/2,0)=(√5/2,0) and (-√5/2,0)
..
slope of asymptotes: ±b/a=±1/(1/2)=±2
equation of asymptotes:
y=-2x
and
y=2x