Stitz-Zeager_College_Algebra_e-book

1 e 1 x 3 y 2 z 2 4 e 2 y 15 z e 3 15y

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Unformatted text preview: x a2 2 2 b b b y b2 = c2 − a2 we get 2 → 2 . This shows that y → ± x as |x| grows large. Thus y = ± x are the x a a a asymptotes to the graph as predicted and our choice of labels for the endpoints of the conjugate axis is justified. In our equation of the hyperbola we can substitute a2 − c2 = −b2 which yields As x and y attain very large values, the quantity a2 − c2 x2 + a2 y 2 = a2 a2 − c2 −b2 x2 + a2 y 2 = −a2 b2 x2 y 2 −2 =1 a2 b The equation above is for a hyperbola whose center is the origin and which opens to the left and right. If the hyperbola were centered at a point (h, k ), we would get the following. Equation 7.6. The Standard Equation of a Horizontala Hyperbola For positive numbers a and b, the equation of a horizontal hyperbola with center (h, k ) is (x − h)2 (y − k )2 − =1 a2 b2 a That is, a hyperbola whose branches open to the left and right If the roles of x and y were interchanged, then the hyperbola’s branches would open upwards and downwards and we would get a ‘vertical’ hyperbola. Equation 7.7....
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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