11 x1 t11 04 chords of a parabola (2013)
TRANSCRIPT
Chords of a Parabola
Chords of a Parabola (1) Chord
Chords of a Parabola (1) Chord
y
x
2 4x ay
Chords of a Parabola (1) Chord
y
x
2 4x ay2(2 , )P ap ap
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
Chords of a Parabola (1) Chord
y
x
2 4x ay
2(2 , )Q aq aq
2(2 , )P ap ap
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
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
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
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
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
(2) Focal Chord (chord passes through focus)
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
(2) Focal Chord (chord passes through focus)
y
x
2 4x ay
2(2 , )Q aq aq2(2 , )P ap ap
0,S a
(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) 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
(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
(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
(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
(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
(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)
(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) 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:
(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
(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