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Lecture 27

# MTH 108 Lecture 27: 9.4 The Hyperbola Notes Premium

3 Pages
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Department
Mathematics
Course Code
MTH 108
Professor
Lun- Yi Tsai

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MTH 108 Precalculus Mathematics II 9.4 The Hyperbola Notes L. Sterling Abstract Provide a generalization to each of the key terms listed in this section*. Hyperbola The general collection of all of the points in the plane. Foci A constant that is also the diﬀerence of the distances from the two ﬁxed points. Transverse Axis The given line that contains the foci. Center The general line segment’s midpoint that is joining the foci. Conjugate Axis The given line that goes through the center and is also perpendicular to the transverse axis. Branches The two separate curves of a hyperbola that are symmetric, but with respect to the traverse axis, center, and the conjugate axis. Vertices The two points of intersection from both the hyperbola and transverse axis. Major Axis’ Length The distance from one vertex to another vertex. 1 Hyperbola Equation: Center at (0;0) Transverse Axis along the X-Axis x2 y2 ▯ = 1 a2 b2 2 2 2 b = c ▯ a Center : (0; 0) Foci : (▯c; 0) and (c; 0) V ertices : (▯a; 0) and (a; 0) Transverse Axis : X ▯ Axis Transverse Axis along the Y -Axis y2 x2 2 ▯ 2 = 1 a b 2 2 2 b = c ▯ a Center : (0; 0) Foci : (0; ▯c) and (0; c) V ertices : (0; ▯a) and (0; a) Tr
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