Year 11 2u locus (1 Viewer)

[kpad5991]

1. find the equation of the locus P that moves such that it is always a distance of 4 units from A (3,1)

2. Find the equation of the locus P that moves such that it is equidistant from A(1,4) and the x axis

 

[Sp3ctre]

1. Let P be the point P(x,y). Using distance formula, find an expression for the distance from (x,y) to (3,1)
sqrt[(x-3)^2 + (y-1)^2] = 4
Square both sides:
(x-3)^2 + (y-1)^2 = 16
Therefore the locus of P is a circle with centre (3,1) and radius 4.

2. Let P be the point P(x,y).
AP = sqrt[(x-1)^2 + (y-4)^2]
Distance between P and y=0 is a vertical distance, |y|
sqrt[(x-1)^2 + (y-4)^2] = |y|
Squaring both sides:
(x-1)^2 + (y-4)^2 = y^2
(x-1)^2 + y^2 - 8y + 16 = y^2
(x-1)^2 = 8y - 16
(x-1)^2 = 8(y-2)