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)
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