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Question 576840: determine the equation of the hyperbola whose asymptotes are y=±2x and which passes through (5/2, 3)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! determine the equation of the hyperbola whose asymptotes are y=±2x and which passes through (5/2, 3)
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given asymptotes show that center of given hyperbola is at (0,0) because y-intercepts of straight line asymptotes=0
center:(0,0)
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Given point thru which hyperbola passes is below the asymptote with the positive slope of 2; therefore, hyperbola has a horizontal transverse axis,and it follows that the slope is ±b/a
b/a=2
b=2a
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Equation:
x^2/a^2-y^2/b^2=1
x^2/a^2-y^2/4a^2=1
LCD:4a^2
4(x^2)-y^2=4a^2
plug in coordinates of given point (5/2,3)
4(5/2)^2-3^2=4a^2
4(25/4)-9=4a^2
25-9=4a^2
16=4a^2
a^2=4
a=2
a^2=4
b=2a=4
b^2=16
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Equation of hyperbola:
x^2/4-y^2/16=1
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