Question 737564
Graph each hyperbola. Identify the verices, foci, and asymptotes 
{{{x^2/4 - y^2/16 = 1}}}
This is a hyperbola that has a horizontal transverse axis (x-term listed first ahead of y-term)
Its standard form of equation: {{{(x-h)^2/a^2-(y-k)^2=1}}}
For given hyperbola:{{{x^2/4 - y^2/16 = 1}}}
center: (0,0)
a^2=4
a=2
vertices: (0±a,0)=(0±2,0)=(-2,0) and (2,0)
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b^2=16
b=4
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c^2=a^2+b^2=4+16=20
c=√20≈4.47
foci: (0±c,0)=(0±4.47,0)=(-4.47,0) and (4.47,0)
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Asymptotes: (equations of lines that go thru center, y=mx+b, m=slope, b= y-intercept)
Slopes of asymptotes of hyperbolas with horizontal transverse axis=±b/a=±4/2=±2
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Equation of asymptote with negative slope=-2
y=-2x+b
b=0
y=-2x
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Equation of asymptote with positive slope=2
y=2x+b
b=0
y=2x
...
y=±(4x^2-16)^.5
See graph below as a visual check:
{{{ graph( 300, 300, -10, 10, -10, 10,(4x^2-16)^.5,-(4x^2-16)^.5,2x,-2x) }}}