M1411001 - y = but there are no y-intercepts(plug in x = to...

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(Chapter 10: Conics) SECTION 10.4: HYPERBOLAS Hyperbolas have two branches. (They may be considered as part of a single branch, if you allow the branches to pass through the point at infinity. Think of a baseball. Don’t worry about this for now!) Technical Note: The locus definition of hyperbolas is similar to the one for ellipses, except that, instead of the sum of the distances to the two foci being kept constant, it is the absolute value of the difference of the distances. The graph of x 2 y 2 = 1 is below: The equation confirms that ± 1 are x -intercepts of the graph (plug in
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Unformatted text preview: y = ), but there are no y-intercepts (plug in x = to see why). The dashed lines are the asymptotes of the hyperbola. The two branches approach those lines but never cross them. (Chapter 10: Conics) The graph of y 2 − x 2 = 1 is below: The equation confirms that ± 1 are y-intercepts of the graph (plug in x = ), but there are no x-intercepts (plug in y = to see why). It helps to remember that: • The graph of x 2 − y 2 = 1 “opens” along the x-axis, while • The graph of y 2 − x 2 = 1 “opens” along the y-axis....
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This note was uploaded on 09/08/2011 for the course MATH 141 taught by Professor Staff during the Fall '11 term at Mesa CC.

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M1411001 - y = but there are no y-intercepts(plug in x = to...

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