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

aqapaqapmPQ 22

22

Chords of a Parabola(1) Chord

y

x

2 4x ay

2(2 , )Q aq aq

2(2 , )P ap ap

aqapaqapmPQ 22

22

2

2qp

qpaqpqpa

Chords of a Parabola(1) Chord

y

x

2 4x ay

2(2 , )Q aq aq

2(2 , )P ap ap

aqapaqapmPQ 22

22

2

2qp

qpaqpqpa

apxqpapy 22

2

Chords of a Parabola(1) Chord

y

x

2 4x ay

2(2 , )Q aq aq

2(2 , )P ap ap

aqapaqapmPQ 22

22

2

2qp

qpaqpqpa

apxqpapy 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

aqapaqapmPQ 22

22

2

2qp

qpaqpqpa

apxqpapy 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 2PQ

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 2PQ

p qm

202

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

(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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

(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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

(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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

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 2PQ

p qm

202

2

ap

aapmPS

pp

appa

21

21

2

2

PSPQ mmPQ

chordfocalaisIf

2212 qp

pp

11 22

pqpqpp

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