11X1 T12 04 chords of a parabola

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<ul><li> 1. Chords of a Parabola </li></ul> <p> 2. Chords of a Parabola (1) Chord 3. Chords of a Parabola (1) Chord y x 2 4ay x 4. Chords of a Parabola (1) Chord y x 2 4ay P(2ap, ap 2 ) x 5. Chords of a Parabola (1) Chord y x 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 ) x 6. Chords of a Parabola (1) Chord y x 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 ) x 7. Chords of a Parabola (1) Chordy x 2 4ayP(2ap, ap 2 )Q(2aq, aq 2 )xap 2 aq 2mPQ 2ap 2aq 8. Chords of a Parabola (1) Chordy x 2 4ay P(2ap, ap 2 )Q(2aq, aq 2 )xap 2 aq 2mPQ 2ap 2aqa p q p q 2a p q pq2 9. Chords of a Parabola (1) Chordy x 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 ) xap 2 aq 2pqmPQ y ap 2 x 2ap 2ap 2aq 2a p q p q 2a p q pq2 10. Chords of a Parabola (1) Chordyx 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 )xap 2 aq 2 pqmPQ y ap 2 x 2ap 2ap 2aq2a p q p q 2 y 2ap 2 p q x 2ap 2 2apq 2a p q pq2 11. Chords of a Parabola (1) Chordyx 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 )xap 2 aq 2 pqmPQ y ap 2 x 2ap 2ap 2aq2a p q p q 2 y 2ap 2 p q x 2ap 2 2apq 2a p q pq p q x 2 y 2apq2 12. (2) Focal Chord (chord passes through focus) 13. (2) Focal Chord (chord passes through focus) y x 2 4ay P(2ap, ap 2 ) Q(2aq, aq 2 )x 14. (2) Focal Chord (chord passes through focus)yx 2 4ay S 0, a 2P(2ap, ap ) Q(2aq, aq 2 )x 15. (2) Focal Chord (chord passes through focus)yx 2 4ay pq1 Prove mPQ 2S 0, a 2P(2ap, ap ) Q(2aq, aq 2 )x 16. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 )Q(2aq, aq 2 ) x 17. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 )a p 2 1 Q(2aq, aq 2 ) x2app2 1 2p 18. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p If PQ is a focal chordmPQ mPS 19. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p If PQ is a focal chordmPQ mPS p2 1 p q2p2 20. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p If PQ is a focal chordmPQ mPS p2 1 p q 2p 2 p 2 1 p 2 pq pq 1 21. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p ORIf PQ is a focal chord (if you have derived equation of chord already)mPQ mPS p2 1 p q 2p 2 p 2 1 p 2 pq pq 1 22. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p ORIf PQ is a focal chord (if you have derived equation of chord already)mPQ mPS 1 p q x 2 y 2apq p2 1 p q 2p 2 p 2 1 p 2 pq pq 1 23. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p ORIf PQ is a focal chord (if you have derived equation of chord already)mPQ mPS 1 p q x 2 y 2apq p2 1 p q 2 (0,a) lies on the chord:2p 2 p 2 1 p 2 pq pq 1 24. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p ORIf PQ is a focal chord (if you have derived equation of chord already)mPQ mPS 1 p q x 2 y 2apq p2 1 p q 2 (0,a) lies on the chord: 2a 2apq 2p 2 pq 1 p 2 1 p 2 pq pq 1 25. (2) Focal Chord (chord passes through focus) yx 2 4aypq 1 Prove mPQ 2 ap a 2 2 mPS S 0, a 2ap 0P(2ap, ap 2 ) a p 2 1 Q(2aq, aq 2 ) x 2ap p2 1 2p ORIf PQ is a focal chord (if you have derived equation of chord already)mPQ mPS 1 p q x 2 y 2apq p2 1 p q 2 (0,a) lies on the chord: 2a 2apq 2p 2 pq 1 p 2 1 p 2 pq Exercise 9E; 1ac, 2, 3, 4, 5, 7 pq 1 </p>