SOLUTION: Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph ((y^2)/(16))-((x^2)/(4))=1

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
***
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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