Question 711898: What are the vertices, foci and asymptotes of the hyperbola with equation 16x^2-4y^2=64
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What are the vertices, foci and asymptotes of the hyperbola with equation 16x^2-4y^2=64
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Standard form of equation for a hyperbola with horizontal transverse axis:
 , (h,k)=(x,y) coordinates of center
divide by 64
center(0,0)
a^2=4
a=2
b^2=16
b=4
..
vertices: (0±a,0)=(0±2,0)=(-2,0) and (2,0)
..
foci:
c^2=a^2+b^2
c^2=4+16=20
c=√20≈4.5
Foci:(0±c,0)=(0±4.5,0)=(-4.5,0) and (4.5,0)
..
Asymptotes: (2 straight lines that go thru center)
slope of asymptotes with horizontal transverse axis: m=±b/a=±4/2=±2
equation of asymptotes:
y=-2x+b
and
y=2x+b
y-intercept, b=0
Equations of asymptotes:
y=-2x
and
y=2x
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