8/3/2019 Hyperbola Derived

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Jeff Bivin -- LZHS

Last Updated: October 11, 2005

8/3/2019 Hyperbola Derived

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Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whosedifference of the distances from two fixedpoints (foci) are constant.

8/3/2019 Hyperbola Derived

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Jeff Bivin -- LZHS

Hyperbola

c2= a2 + b2

8/3/2019 Hyperbola Derived

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Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whose difference of thedistances from two fixed points (foci) are constant.

8/3/2019 Hyperbola Derived

5/13

Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whose difference of thedistances from two fixed points (foci) are constant.

8/3/2019 Hyperbola Derived

6/13

Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whose difference of thedistances from two fixed points (foci) are constant.

8/3/2019 Hyperbola Derived

7/13Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whose difference of thedistances from two fixed points (foci) are constant.

8/3/2019 Hyperbola Derived

8/13Jeff Bivin -- LZHS

Hyperbola

The set of all co-planar points whose difference of thedistances from two fixed points (foci) are constant.

8/3/2019 Hyperbola Derived

9/13Jeff Bivin -- LZHS

Hyperbola

P

F2F1

(x, y)

(-c, 0) (c, 0)(0, 0)

aoycxoycx 2)()()()]([(2222

aycxycx 2)()(

2222

PF1 - PF2 = 2a

8/3/2019 Hyperbola Derived

10/13Jeff Bivin -- LZHS

aycxycx 2)()(2222

2222 )(2)( ycxaycx

222222 )(2)( ycxaycx 2222222 )()(44)( ycxycxaaycx

22222222)(442 cxcxycxaacxcx

222 )(444 ycxaxca

222)( ycxaxca

4

8/3/2019 Hyperbola Derived

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222)( ycxaxca

2

2222 )( ycxaxca

2222224 )(2 ycxacxxcaa

22222224 22 ycxcxacxxcaa

2222222222422 yacaxcaxacxxcaa

222222224yacaxacxa

8/3/2019 Hyperbola Derived

12/13Jeff Bivin -- LZHS

222222224yacaxacxa 222 bacthatremember

22222222224 yabaaxabaxa 222242222224

yabaaxaxbxaa

222222yabaxb

222222bayaxb

22

22

22

22

22

22

baba

baya

baxb

12

2

2

2

b

y

a

x

22ba

8/3/2019 Hyperbola Derived

13/13Jeff Bivin -- LZHS

)0,0(atcenterahasthis

12

2

2

2

b

y

a

x

),( khatiscentertheif

1

2

2

2

2

b

ky

a

hx