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Lesson29_students_ - MA 15400 Lesson 29 Section 11.3...

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MA 15400 Lesson 29 Section 11.3 Hyperbolas 1 A hyperbola is the set of all points in a plane, the difference of whose distances from two fixed points (the foci ) in the plane is a positive constant. The midpoint of the two foci is the center of the hyperbola. (Centers are marked with C.) The foci are c units from the center. The points where the hyperbola intersects the line joining the foci are the vertices . The vertices are a units from the center. In a hyperbola c > a , where in an ellipse a > c . There are two axes: 1) The line segment V'V is the transverse axis . The foci lie beyond the endpoints of the transverse axis. The length of a transverse axis is 2 a . 2) The graph does not cross the other axis, the conjugate axis . Its endpoints, W and W', are not points on the hyperbola, however, are very important in creating an auxiliary rectangle that assists in sketching the graph. The length of a conjugate axis is 2 b . (See the next page.) There are two ‘branches’ of a hyperbola. If the foci are on a horizontal line, the ‘branches’ are opening left and right. If the foci are on a vertical line, the ‘branches’ are opening up and down. The foci will lie ‘inside’ the ‘branches’.
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