SOLUTION: write the equation for the following asymptotes for the following hyperbola x^2-4y^2=16

Question 596617: write the equation for the following asymptotes for the following hyperbola x^2-4y^2=16
Found 2 solutions by jsmallt9, lwsshak3:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First let's put the equation in standard form:

Dividing by 16 (to get the 1 on the right):

Since x = x - 0 and y = y - 0, we can make these substritutions (so we can see the full form):

We can now see that the center is (0, 0) and that and making a = 4 and b = 2. And since the x is before the minus, this is a horizontally-oriented hyperbola.

With horizontally-oriented hyperbolas, the slopes of the asymptotes are b/a and -b/a, making the slopes for your asymptotes 2/4 and -2/4 or, in reduced form, 1/2 and -1/2.

The asymptotes pass through the center of the hyperbola. So your asymptotes will be:
a line passing through (0, 0) with a slope of 1/2; and
a line passing through (0, 0) with a slope of -1/2

Writing the equations of these lines will be very easy because (0, 0) is not just any point on the asymptotes, but it is the y-intercept for both asymptotes (since the x-coordinate is 0). So we can directly write the slope-intercept forms of these equations:
or simply
and
or simply
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
write the equation for the following asymptotes for the following hyperbola x^2-4y^2=16
divide by 16
x^2/16-y^2/4=1
This is an equation for a hyperbola with horizontal transverse axis of the standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center:(0,0)
a^2=16
a=√16=4
..
b^2=4
b=2
..
slopes of asymptotes, m: �b/a=�2/4=�1/2
equations of asymptotes:
y=mx+b and y=-mx+b, m=slope, b=y-intercept
y=x/2+b and y=-x/2+b
since asymptotes go thru origin, (0,0), y-intercept,b=0
equations therefore are:
y=x/2 and y=-x/2
RELATED QUESTIONS
what are the equations for both asymptotes of the following hyperbola... (answered by lwsshak3)
Hello, could someone please help me with the following problem? I am supposed to provide (answered by MathLover1)
I'm having trouble with these! Help? For the following equation of a hyperbola,... (answered by Fombitz)
For the following hyperbola: (x + 1)2 � (y � 3)2 = 1 (answered by lwsshak3)
Find the center, vertices, foci and asymptotes for the hyperbola 25x^2 - 4y^2 =... (answered by ikleyn)
Identify the vertices, foci, and slope of the asymptotes for the hyperbola x^2/25 -... (answered by lwsshak3)
graph the hyperbola with the following equation.... (answered by Alan3354)
Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the... (answered by ewatrrr)
Find the coordinate of the vertices and foci and the equation of the asymptotes for the... (answered by ikleyn)