Ellipse Derived
of 21
-
Upload
oerallys-vhyto -
Category
Documents
-
view
233 -
download
0
Transcript of Ellipse Derived
-
8/3/2019 Ellipse Derived
1/21
Jeff Bivin -- LZHS
Last Updated: April 11, 2006
-
8/3/2019 Ellipse Derived
2/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
3/21
Jeff Bivin -- LZHS
Ellipse
a2 = b2 + c2
-
8/3/2019 Ellipse Derived
4/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
5/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
6/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
7/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
8/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
9/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
10/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
Sum of the distances from any point on anellipse to the two foci is 2a
-
8/3/2019 Ellipse Derived
11/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
12/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
13/21Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
14/21
Jeff Bivin -- LZHS
EllipseP
F2F1
PF1 + PF2 = 2a
(0, 0)
(x, y)
(-c, 0) (c, 0)
aoycxoycx 2)()()()]([(2222
aycxycx 2)()( 2222
-
8/3/2019 Ellipse Derived
15/21
Jeff 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 Ellipse Derived
16/21
Jeff Bivin -- LZHS
222)( ycxaxca
2
2222 )( ycxaxca
2222224 )(2 ycxacxxcaa
22222224 22 ycxcxacxxcaa
2222222222422 yacaxcaxacxxcaa
222222224yacaxacxa
-
8/3/2019 Ellipse Derived
17/21
Jeff Bivin -- LZHS
222222224yacaxacxa
222222 baccbathatremember
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 Ellipse Derived
18/21
Jeff Bivin -- LZHS
)0,0(atcenterahasthis
12
2
2
2
b
y
a
x
),( khatiscentertheif
1
2
2
2
2
b
ky
a
hx
-
8/3/2019 Ellipse Derived
19/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
20/21
Jeff Bivin -- LZHS
Ellipse
The set of all co-planar points whose sumof the distances from two fixed points (foci)are constant.
-
8/3/2019 Ellipse Derived
21/21
Jeff Bivin -- LZHS
Ellipse
a2 = b2 + c2
