Locus

WMY_hk, Feb 15, 2023

Locus

Table of Contents

  1. Sketch the locus
    1. Locus 1 (fixed distance from a fixed point)
    2. Locus 2 (a fixed distance from a straight line)
    3. Locus 3 (equidistant from 2 straight lines)
    4. Locus 4 (equidistant from 2 points)
    5. locus 5 (fixed distance from line segment)
    6. Locus 6 (2 line segments perpendicular)
    7. Locus 7 (Fixed ratio of distance between 2 points)
    8. Locus 8 (equidistant from a fixed point and a straight line)
  2. Find the equation of the locus
    1. Revision on equation of Straight line
    2. Equation of Circle
    3. 小測試

1.

Sketch the locus

  • 1. Locus 1 (fixed distance from a fixed point)
  • 2. Locus 2 (a fixed distance from a straight line)
  • 3. Locus 3 (equidistant from 2 straight lines)
  • 4. Locus 4 (equidistant from 2 points)
  • 5. locus 5 (fixed distance from line segment)
  • 6. Locus 6 (2 line segments perpendicular)
  • 7. Locus 7 (Fixed ratio of distance between 2 points)
  • 8. Locus 8 (equidistant from a fixed point and a straight line)

1.1.

Locus 1 (fixed distance from a fixed point)

Definition of Locus 軌跡的定義
A locus is a path formed by a collection of points which satisfy one or more given conditions.[br]軌跡是一條由點構成的路徑，這些點均滿足某單一條件或同時滿足多個條件。
1. A moving point P is 3 units from a fixed point Q. Mark all the positions that P can be.
2. what is the locus of the point P？(i.e. 所有P點組成的形狀）
3. Describe the locus of P. e.g. length，width，height，radius，centre
– WMY_hk

1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

Find the equation of the locus

  • 1. Revision on equation of Straight line
  • 2. Equation of Circle
  • 3. 小測試

2.1.

Revision on equation of Straight line

Consider the straight line passing through points A and B. C is a point on the straight line. 考慮穿過A，B兩點的直綫。C是綫上一點。
1. Let C be (x,y).
[size=150](a) From the graph, Which of the following conditions does C satisfy? [br]  由圖中可得，點C滿足以下哪個條件?[/size]
[size=100][size=150](b) From (a), determine which of the following equations does C satisfy? [br]  由(a)，點C滿足以下哪條等式?[/size][/size]
[size=150][size=200]Since every points on the straight line satisfy the equation above, the equation above is the equation of the straight line.[br]因爲直綫上的任意點均滿足上述式，因此上述式就是這條直綫的方程。[/size][/size]
2. 透過化簡上述式，可得以下直綫方程。
Conclusion
[size=150][size=200]Therefore, to find the equation of any shape, we just need to find an equation that every points on the shape satisfy.所以，求任意圖形的方程，我們衹需要找出圖形上任意點都滿足的一條等式。[/size][/size]
– WMY_hk

2.2.

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2.3.

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