Advanced Precalculus Notes 9.4 The Hyperbola

Hyperbola: The set of all points in a plane, the difference of whose distances from two distinct fixed points (foci) is a constant.

Transverse axis: line containing center and foci. Conjugate axis: line perpendicular to transverse

axis, passing through the center.

Center: (h, k) Center: (h, k) Vertices: (h ± a, k) Vertices: (h, k ± a) Foci: (h ± c, k) Foci: (h, k ± c)

1)()(

2

2

2

2

b

ky

a

hx 1)()(

2

2

2

2

b

hx

a

ky

)( hxa

bky )( hx

b

aky

222 bac

Graph the hyperbola:

Label the center, vertices, foci and asymptotes. Center: Vertices: Foci: Asymptotes:

194

22

yx

Find an equation of the hyperbola with center at the origin, one focus at (3, 0), and one vertex at (-2, 0).

Discuss the equation: Center: Vertices: Foci: Asymptotes:

44 22 xy

Discuss the equation: Center: Vertices: Foci: Asymptotes:

0111624 22 yxyx

Find an equation for the hyperbola with center at (1, -2), one focus at (4, -2), and one vertex at (3, -2).

Suppose that two people standing 1 mile apart both see a flash of lightning. After a period of time, the person standing at point A hears the thunder. One second later, the person standing at point B hears the thunder. If the person at B is due west of the person at A and the lightning strike is known to occur due north of the person standing at point A, where did the lighting strike?

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