## 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 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)

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