Question 640957: find an equation of the specified hyperbola with center at the origin.
with given Foci : ( +-10,0) ; Asymptotes: y=+-3/4x Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! find an equation of the specified hyperbola with center at the origin.
with given Foci : ( +-10,0) ; Asymptotes: y=+-3/4x
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Give data shows this is a hyperbola with horizontal transverse axis.
Its standard form of equation: , (h,k)=(x,y) coordinates of center
Given center: (0,0)
Given slope of asymptotes=±3/4
For hyperbolas with horizontal transverse axis, slope of asymptotes=b/a=3/4
3a=4b
b=3a/4
Given Foci=±10
c=10
c^2=100=a^2+b^2=a^2+(3a/4)^2
a^2+9a^2/16=100
LCD:16
16a^2+9a^2=1600
25a^2=1600
a^2=1600/25=64
b^2=9a^2/16=9*64/16=36
Equation of given hyperbola:
(