SUEC ¸ßÖÐ Adv Maths (Locus) (Part 1).pptx
- 2. ?? ??
- 3. ?? ??
- 4. ?? ?? 5
- 5. ?? ?? ?1 , ?1 ?2 , ?2
- 6. ?? ?? ?(2,1)
- 7. ?? ?? ? = 2 5 ? = 0 ?2 + ?2 = ?2 ?2 ? 8? + 16 = 0 ?2 + ?2 = 5 ? = ?
- 8. ?2 ? 8? + 16 = 0 ??? ? = (?, ?) ? ???? = (?, 0) ?? = ? ? ???? ? (0, 4) ?2 + ? ? 4 2 = ?2 ?2 + ?2 ? 8? + 16 = ?2 ?2 + ?2 = 5 ?? 2 + ?? 2 = 42 ??? ? = (?, ?) ? ? 4 2 + ?2 + ? + 4 2 + ?2 = 42 ?2 + 16 ? 8? + ?2 + ?2 + 16 + 8? + ?2 = 42
- 9. 2?? = 2?2 ?? 2 ? ?? 2 = ?2 ??? ? = (?, ?) ?2 + ?2 ? ? ? ? 2 + ?2 = ?2 ?2 + ?2 ? ?2 + ?2 ? 2?? + ?2 = ?2 ? = ? 3?2 + 3?2 ? 2? ? 20? + 27 = 0 ??? ? = (?, ?) ? = (3,2) ? = (1,3) ?? = 2?? ? ? 3 2 + ? ? 2 2 = 2 ? ? 1 2 + ? ? 3 2 ?2 + 9 ? 6? + ?2 + 4 ? 4? = 4 (?2 + 1 ? 2? + ?2 + 9 ? 6? ? ? 3 2 + ? ? 2 2 = 4 ? ? 1 2 + ? ? 3 2
- 10. ?? ?? 3?2 + 3?2 ? 2? ? 20? + 27 = 0 ?2 + ?2 = 4 ?2 + ?2 ? 8? ? 8? + 7 = 0
- 11. ??? ? = (?, ?) ??? ¡Á ??? = ?1 ? ? ? 1 ¡Á ? ? 8 ? ? 7 = ?1 ?2 ? 8? = ? ?2 + 7 ? 8? ?? ?? ?2 + ?2 ? 8? ? 8? + 7 = 0
- 12. ?? ?? ?????? & ??????
- 13. ?? ?? ? ? 3 2 + ? + 2 2 = 36 ?2 + ?2 = 25 9 ? ? 8 2 + ? + 3 2 = 25 ? ? ? 2 + ? + ? 2 = ? + ? 2
- 14. ?? ?? ? ?? ???????? ???? ?? = ????????
- 15. ?? ?? ???????? ???? ?? = ????????
- 16. ?? ??
- 17. ?? ??
- 18. ?? ?? ??????? ?1 , ?1
- 19. ?? ?? ? + 6 2 + ? ? 3 2 = 10 ? ? 5 2 + ? + 3 2 = 13 | ?? | = 5 2
- 20. ?? ?? | ?? | = 5 2 ? ? = ???????? ?? ?? = (5, ?3) ? = 13
- 21. ?? ?? ?2 + ? ? 5 2 = 34 ? ? 4 2 + ?2 = 25 ? + 5 2 + ? ? 4 2 = 16 ? ? 1 2 + ? + 3 2 = 13 ? ? 18 2 + ? ? 16 2 = 100 ? ? 2 2 + ? ? 4 2 = 100
- 22. ?? ?? ? ? 18 2 + ? ? 16 2 = 100 ? = ? = 4? + 3? ? 70 5 = 10 (10, 10) ?1 ¡Ã 4? + 3? ? 70 = 0 , ? = 4 3 ?2 ¡Ã ? ? 10 = 3 4 (? ? 10) 4? ? 3? ? 10 = 0 ? ?¢Ù 4? + 3? ? 120 = 0 ? ?¢Ú ?? 4? + 3? ? 50 = 0 ??? ?? ???? ???????? ?? ???? ??? ?? ???????? ????? ????? ?????? ?? ????????? ??? ¢Ù ??? ¢Ú
- 23. ?? ?? ? ? ? ?? = ?? = ? = 10 ¡à ? = ?????? = ???????? ?? ?? ? = (5, ?1)
- 24. ?? ??
- 25. ?? ??
- 26. ?? ??
- 27. ?? ??
- 28. ?? ?? 3?2 + 3?2 + 24? + 82? = 0 ?2 + ?2 ? ?? ? ?? = 0 25?2 + 25?2 ? 277? ? 83? ? 278 = 0 ?2 + ?2 ? 8? ? 2? + 12 = 0
- 29. ?? ?? 2 ???????????? ??????
- 30. ?? ?? 2 ???????????? ?????? ? ? ?
- 31. ?? ?? ? ?? ?? ?? ????? ???? ? ????? ?? ??? ????? ?? ? ????? 0 (0, 0) ??? ? (3, 0) ????? ???????? ????? ?? 1 2 . ???? ??? ???????? ?? ???? ????? ??? ???? ??? ?????.
- 32. ?? ?? 2?2 + 2?2 ? 11? ? 19? + 44 = 0 ?2 + ?2 ? ?? ? ?? = 0 ?2 + ?2 ? 8? ? 9 = 0 ?2 + ?2 ? 2? = 0 2?2 + 2?2 ? 21? + 8? + 60 = 0
- 33. ?? ?? 2?2 + 2?2 ? 11? ? 19? + 44 = 0 ? ????????? ? + ? = 4 ??? ??? ? ? ???? ? = (0, 4) ?????????? ?, ?, ? ???? ? ¡Ã 4 + 4 + 4? + 4? + ? = 0 8 + 4? + 4? + ? = 0 ? ?¢Ù ? ¡Ã 25 + 9 + 10? + 6? + ? = 0 34 + 10? + 6? + ? = 0 ? ?¢Ú ? ¡Ã 16 + 8? + ? = 0 ? ?¢Û
- 34. ?? ?? ¡à ?2 +?2 ? ?? ? ?? = 0 ??? ? & ? = ??????????? ?? ??? ? & ? ????. ?????????? ??? ??????????? ???? ?????? ¡Ã ? = 0 ? ¡Ã ?2 + 2?? = 0 ? ¡Ã ?2 + 2?? = 0 ? = (?, 0) , ? = (0. ?) 2? = ? 2? = ??
- 35. ?? ?? ?2 + ?2 = ?2
- 36. ?? ?? ?2 + ?2 = ?2 ??? ? = (?, ?) = ???????? ?? ?? ¡à ? = (2?, 0), ? = (0, 2?) ?? = 2? 2 + 2? 2 = 2? 2? 2 + 2? 2 = 4?2
Editor's Notes
- #2: https://www.onlinemathlearning.com/locus-math.html
- #9: 5. Knowing that the distance from point P to the x-axis is equal to its distance from point F (0, 4), find the orbital equation of point P. 6. Given that the sum of the squares of the distance between point P and point A (4,0) and point B (-4, 0) is 42. find the orbital equation of point P.
- #10: 9. The distant from a moving point to point (3,2) is equal to twice the distance to point (1,3).
- #12: The central angle APB formed by a moving point P and 2 fix points A (1,0) & B (7,8) is always a right angle.
- #23: r = 10, tangent to line 4x+3y-70 = 0 at point (10,10). Find eq
- #24: The coordinates of vertex A of an isosceles triangle are (4,2) and the coordinates of one endpoint B of the base (3.5). Find the eq at the other endpoint C and explain.
- #34: A circle passes through the points A (2, 2), B (5, 3), and passes through the intersection of the line x + y = 4 and the y-axis, find the equation of this circle.
- #35: A circle passed through the origin of coordinates and the intercepts on the x-axis and y-axis are a and b respectively. Find the equation of this circle.
- #37: A line segment | AB | = 2a, its two endpoints A and B slide on the x-axis and y-axis respectively, find the orbit of the midpoint P of AB.