Question 659134: Find the equation of hyperbola whose vertices are (0,0) and (10,0) and one of its foci is (18,0).Also find its asymptotes? Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the equation of hyperbola whose vertices are (0,0) and (10,0) and one of its foci is (18,0).Also find its asymptotes?
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This is a hyperbola with horizontal transverse axis:
Its standard form of equation:
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center: (5,0)
length of horizontal transverse axis=10 (0 to 10)=2a
a=5
a2=25
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c=18 (distance from center to one of foci)
c^2=324
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c^2=a^2+b^2
b^2=c^2-a^2=324-25=299
b=√299≈17.3
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equation of given hyperbola:
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slopes of asymptotes=±b/a=±17.3/5≈±3.46
asymptotes are lines that go thru the center and are of the form: y=mx+b, m=slope, b=y-intercept
equation of asymptote with slope<0
y=-3.46x+b
solve for b using coordinates of center
0=-3.46*5+b
b=17.33
equation:y=-3.46x+17.33
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equation of asymptote with slope>0
y=3.46x+b
solve for b using coordinates of center
0=3.46*5+b
b=-17.33
equation:y=3.46x-17.33
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