Question 623488: What is the standard form of the hyperbola with foci at (±4,0) and vertices at (±3,0)?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! What is the standard form of the hyperbola with foci at (±4,0) and vertices at (±3,0)?
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This is an equation of a hyperbola with horizontal transverse axis:
Its standard form of equation: (x-h)^2,a^2-(y-k)^2=1, (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (0,0)
From vertices,length of transverse axis=6=2a
a=3
a^2=9
..
From foci, 2c=8
c=4
c^2=16
..
c^2=a^2+b^2
b^2=c^2-a^2=16-9=7
b=√7
..
Equation:
x^2/9-y^2/7=1
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