Question 594112: Write an equation for the conic section:
A hyperbola with foci at (-3,0) and (3,0) and vertices at (2,0) and (-2,0).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation for the conic section:
A hyperbola with foci at (-3,0) and (3,0) and vertices at (2,0) and (-2,0).
**
Equation is that 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)
length of horizontal transverse axis=4 (-2 to 2)=2a
a=2
a^2=4
..
2c=6 (-3 to 3)
c=3
c^2=9
..
c^2=a^2+b^2
b^2=c^2-a^2=9-4=5
..
Equation:
x^2/4-y^2/5=1
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