Question 848088: Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph ((y^2)/(16))-((x^2)/(4))=1
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph
((y^2)/(16))-((x^2)/(4))=1
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This is an equation of a hyperbola with vertical transverse axis.
Its standard form of equation:  , (h,k)=(x,y) coordinates of center.
center: ((0,0)
a^2=16
a=4
vertices: (0±a,0)=(0±4,0)=(-4,0) and (4,0)
b^2=4
b=2
c^2=a^2+b^2=16+4=20
c≈√20≈4.5
foci: (0±c,0)=(0±4.5,0)=(-4.5,0) and (4.5,0)
slope of asymptotes=±a/b=±4/2=±2
Equation of asymptotes:
y=2x
y=-2x
see graph below:
y=4(1+x^2/4)^.5
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