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Stitz-Zeager_College_Algebra_e-book

# That is amount of 30 stock solution amount of 90

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Unformatted text preview: at b the slopes of the asymptotes are ± a . Since a = 5 and the slope of the line y = 2x is 2, we have b that 5 = 2, so b = 10. Hence, b2 = 100 and our ﬁnal answer is x2 y2 − =1 25 100 As with the other conic sections, an equation whose graph is a hyperbola may be given in a form other than the standard forms in Equations 7.6 or 7.7. In those cases, as with conic sections which have come before, we will need to massage the given equation into one of the forms in Equations 7.6 or 7.7. To Write the Equation of a Hyperbola in Standard Form 1. Group the same variables together on one side of the equation and position the constant on the other side 2. Complete the square in both variables as needed 3. Divide both sides by the constant term so that the constant on the other side of the equation becomes 1 Example 7.5.3. Consider the equation 9y 2 − x2 − 6x = 10. Put this equation in to standard form and graph. Find the center, the lines which contain the transverse and conjugate axes, the vertices, the foci, and the equations of the asymptotes. Solution. We need only complete the square on the x, and then divide, if necessary, to get the...
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