SOLUTION: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (4,0) or (-4,0) Asymptotes: y=4x or y=-4x

Question 607485: Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (4,0) or (-4,0) Asymptotes: y=4x or y=-4x
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the standard form of the equation of the hyperbola with the given characteristics. Foci: (4,0) or (-4,0) Asymptotes: y=4x or y=-4x.
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This is an equation of a hyperbola with horizontal transverse axis.
Its 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)
From foci data:
c=4
c^2=16
..
slope of asymptote=b/a=4
b=4a
..
c^2=a^2+b^2
=a^2+(4a)^2
=a^2+16a^2
=17a^2
..
c^2=17a^2=16
a^2=16/17
a=4/√17
.
b=4a=16√17
b^2=256/17
..
Equation:
x^2/(16/17)-y^2/(256/17)=1

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