Equations of locus

1. Find the eq. of the locus of a point which is at a constant distance 4 units
from the line 3x +4y -10 = 0.

Ans:
let (x,y) is the moving point which is on the equation ,

(3x+4y-10)/5=+/-4
3x+4y-10=+/-20

so the equation of the locus of a point which is at a constant distance 4 units from the line 3x +4y -10 = 0 are 3x+4y+10=0 and 3x+4y-30=0//


2008-07-13 15:43:36 補充：
2. A point P moves so that its distance from (2,3) is always equal to its distance from the line x +2 = 0

ANs:
let the point P is (x,y)

x-(-2)=((x-2)^2+(y-3)^2)^(1/2)
x^2+4x+4=x^2-4x+4+y^2-6y+9
y^2-6y-8x+9=0//

2008-07-13 15:45:26 補充：
3. A ponit P moves in such a way that its distance from the point (4,0) is equal to its distance from the line x +y = 0.Find the eq. of the locus of P.

let P is (x,y)

((x-4)^2+(y-0)^2)^(1/2)=(x+y)/(2)^(1/2)
x^2-8x+16+y^22=(x^2+2xy+y^2)/2
x^2+y^2-8x+2xy+16=0//