11 x1 t11 04 chords of a parabola (2012)
-
Upload
nigel-simmons -
Category
Education
-
view
263 -
download
1
Transcript of 11 x1 t11 04 chords of a parabola (2012)
![Page 1: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/1.jpg)
Chords of a Parabola
![Page 2: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/2.jpg)
Chords of a Parabola (1) Chord
![Page 3: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/3.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
![Page 4: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/4.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay2(2 , )P ap ap
![Page 5: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/5.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
![Page 6: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/6.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
![Page 7: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/7.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
aqap
aqapmPQ
22
22
![Page 8: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/8.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
aqap
aqapmPQ
22
22
2
2
qp
qpa
qpqpa
![Page 9: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/9.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
aqap
aqapmPQ
22
22
2
2
qp
qpa
qpqpa
apxqp
apy 22
2
![Page 10: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/10.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
aqap
aqapmPQ
22
22
2
2
qp
qpa
qpqpa
apxqp
apy 22
2
apqapxqpapy 2222 22
![Page 11: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/11.jpg)
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
aqap
aqapmPQ
22
22
2
2
qp
qpa
qpqpa
apxqp
apy 22
2
apqapxqpapy 2222 22
apqyxqp 22
![Page 12: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/12.jpg)
(2) Focal Chord (chord passes through focus)
![Page 13: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/13.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
![Page 14: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/14.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
![Page 15: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/15.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
![Page 16: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/16.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
![Page 17: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/17.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
![Page 18: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/18.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
![Page 19: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/19.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
![Page 20: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/20.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
![Page 21: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/21.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
OR
(if you have derived equation of chord already)
![Page 22: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/22.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
OR
(if you have derived equation of chord already)
1 apqyxqp 22
![Page 23: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/23.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
OR
(if you have derived equation of chord already)
1 apqyxqp 22
2 (0,a) lies on the chord:
![Page 24: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/24.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
OR
(if you have derived equation of chord already)
1 apqyxqp 22
2 (0,a) lies on the chord:
1
22
pq
apqa
![Page 25: 11 x1 t11 04 chords of a parabola (2012)](https://reader033.fdocuments.net/reader033/viewer/2022042818/55b859cfbb61eb04238b45a3/html5/thumbnails/25.jpg)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
1 Prove 2
PQ
p qm
2 02
2
ap
aapmPS
p
p
ap
pa
2
1
2
1
2
2
PSPQ mm
PQ
chord focal a is If
22
12 qp
p
p
1
1 22
pq
pqpp
OR
(if you have derived equation of chord already)
1 apqyxqp 22
2 (0,a) lies on the chord:
1
22
pq
apqa
Exercise 9E; 1ac, 2, 3, 4, 5, 7