# 10.4-one - 4.4 The Hyperbola A hyperbola is the collection...

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Unformatted text preview: ' 4.4 The Hyperbola A hyperbola is the collection of all points in the plane, the difference of those distances from two fixed points, called the foci, is a constant. “ilru imp. Carriages Hm foe} is Calieoi sine 'iTQmsvevse axis. midpofnvi fo-Jnd‘ry Hm Conjugate ax's Transverse axis *Foei E‘s «imaginiqr e; he law-armhole. m Um). "ihTDUeSI-i “'H'u; Camiev amd Pevpmdc‘celqr « 0 Ha +‘romsverrse 6005—3 TS: aim Cpn‘wéah axis. Tia h pevboler has "iwo SePavo‘tid Ctu'wis Coiled BTGMICLQ/ ‘i’iuuj mﬁ-qmmea‘m’e W--'Y- +0 VHUL 'WSVOJYSL art‘s/Cory).qu 1. Analyze Hygerbolas with Center at the Origin ax“ and Why. The +000 Poi‘nis 0-? y tinimrsecigm 0-? W QU-nci «HAIL Transverse axis HWSVQYSQ axis, Gert Fi . F2={C.0)X F2 P= My) din. P) d(F1.P) — d(F3. P) = :i:2a Equation of a Hyperbola Center at (O, 0) Transverse Axis along the x—Axis An equation of the hyperbola with center at (O, O). foci at (—C. 0) and (c. 0). and vertices at (ma. 0) and (a. 0) is V1 = (-3.0) Transverse axis The transverse axis is the x—axis. Equation of a Hyperbola; Center at (O, 0); Transverse Axis along the y-Axis An equation of the hyper-bola with center at (0. 0). foci at (0. Mc) and (0. c). and vertices at (0. —a) and (0. a) is The transverse axis is the y—axis. 2. Find the Asymptotes of a Hyperbola Asymptotes of a Hyperbola I )7 . The hyperbola —, - = 1 has; the two 0131qu asymploEes a- _ Asymptotes of a Hyperbola The hyperbola — Z—; = 1 has the two oblique asymptotes a- _ ASWFJro-{reg PW'DN; (£2 in £07m a'h"tm 63130126" W m O~\$kjwi>3tol15 6L Pwkbota. OUer YLO+ Dow): "HAIL Mﬁbob/ do Scam/1L 0L8 CL {01 Ck HPQ'TIDOIQ. 3. Analyze Hyperbolas with Center at (h, k} HYPERBOLAS WITH CENTER AT (11, R) AND TRANSVERSE AXIS PARALLEL TO A COORDINATE AXIS \— — ——wr I\ I] l I 1 Transverse F1V \ ’ V F2 axis Transverse Axis Foci Vertices Equation Asymptotes Parallel to the 2 2 x — h — k x-axis (hick) {hia,k) l zl—(yb2)=1. b1=c2—02 y—k:i%(x—h) _ A Parallel to the 2 2 — k x - h y-axis (lukic) (h.kia) (y )ﬁl b2) :1. laz=c2~lri2 y—k=;tg(x—h) \ y f y Transverse \ / \ / \ (h. k) / ><Y m) Find em Wm 76w (ML ksza bola. mama, 6.me (0,0) Foam (5,?) vm+ax (he), Xlﬂ_ HLnt bl: 8:41;" _.__.— __l__...r-— (11' E3; ...
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## This note was uploaded on 01/16/2012 for the course MATH 127 taught by Professor Blisinhestiyas during the Fall '11 term at Truckee Meadows Community College.

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10.4-one - 4.4 The Hyperbola A hyperbola is the collection...

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