週六, 14 四月 2018 16:00

20 Days to Go(-2 Days) Locus

The coordinates of the points A and B are (1,4) and (5,12) respectively. It is given that C is a point on the line segment AB such that AC:BC= 1:3 . L is a horizontal line passing through C.
 
(a) Find the coordinate of C
(b) Find the equation of L
(c) P is a moving point in the rectangular coordinate plane such that the distance between P to B is equal to the perpendicular distance between P to L. Denote the locus of P by Г.

    (i) Find the equation of Г.
    (ii) Describe the Г .
    (iii) The Г and AB intersect at D. Find the coordinate of D .
    (iv) The lowest point of Г, denoted by K, Find the area of BDK

 
 

locus 1

       locus 2

 

Locus 主要有6大類考法:

- Maintaining a fixed distance from a fixed point (Circle)

- Maintaining an equal distance from two given points (Perpendicular Bisector)

Maintaining a fixed distance from a line (Two parallel lines)

Maintaining a fixed distance from a line segment (Field track)

Maintaining an equal distance from two parallel lines (A parallel straight line)

Maintaining an equal distance from two intersecting lines (A pair of angle bisector)

 

但其實仲有一類大家都應該要識 , 不過可能同學仔已經遺忘左 , 就係上面例題出現嘅一種

Maintaining an equal distance from a point and a straight line (Parabola)

呢一類係近年DSE都無出現過 , 所以大家溫習時都應該要特別留意

 

 

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