SOLUTION: i need to find the asymptotes of: (x/4)2-(y/2)2=1 the 2 after the parenthesis means its squared. i know the equation is y=b/a x, and y=-b/a x so a = root 2 and b= root 2, is th

Question 413360: i need to find the asymptotes of:
(x/4)2-(y/2)2=1
the 2 after the parenthesis means its squared.
i know the equation is y=b/a x, and y=-b/a x
so a = root 2 and b= root 2, is the answer 1?, can you better explain how to solve the problem?
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
i need to find the asymptotes of:
(x/4)2-(y/2)2=1
..
Standard form of given hyperbola is: x^2/a^2-y^2/b^2=1
What you have here is:
x^2/16-y^2/4=1
This is a hyperbola with center at (0,0) that open sideways, that is, its transverse axis is horizontal.
a^2=16
a=4
b^2=4
b=2
like you said, the equations of the asymptotes are: y=b/ax and-b/ax.
For the given hyperbola, y=(2/4)x and y=-(2/4)x
See the graph below for a visual picture of the asymptotes. You might note that equations of the asymptotes are equations of straight lines of standard form, y=mx+b, with the y-intercept=0 and the slopes, m=b/a and m=-b/a
..
y=((x^2-16)/4)^.5

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