Question 618961: Find the standard form of the equation of the specified hyperbola. Graph and Label.
Vertices (+ or -2,0)
Asymptotes y = +or- 1/2x Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the standard form of the equation of the specified hyperbola. Graph and Label.
Vertices (+ or -2,0)
Asymptotes y = +or- 1/2x
**
Given hyperbola has a horizontal transverse axis:
Equation: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center.
For given hyperbola:
center: (0,0)
length of horizontal transverse axis=4 (-2 to 2)=2a
a=2
a^2=4
..
slope of asymptotes for hyperbolas with horizontal transverse axis=b/a=1/2
b=a/2=2/2=1
b^2=1
..
Equation of given hyperbola:
x^2/4-y^2=1
see graph below: (I don't have the means to label the graph in detail, but it is a good visual check of what the curve should look like)
y=±(x^2/4-1)^.5
(