locus (1 Viewer)

205021 · May 23, 2009

The distance of a point from the line x=4 is equal to its distance from y=1. Find the equation of the locus.

I know there are two answers, I just keep ending up with x + y = 5 and not getting x - y = 3. How do I solve this properly?

kurt.physics · May 23, 2009

205021 said:
The distance of a point from the line x=4 is equal to its distance from y=1. Find the equation of the locus.

I know there are two answers, I just keep ending up with x + y = 5 and not getting x - y = 3. How do I solve this properly?

$Let this point be (x,y)$

$Using the distance formula$

$d = \sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}$

$\sqrt{(x - 4)^2 + (y - y)^2} = \sqrt{(x - x)^2 + (y - 1)^2}$

$(x - 4)^2 + (y - y)^2 = (x - x)^2 + (y - 1)^2$

$(x-4)^2 = (y-1)^2$

$(x-4)^2 - (y-1)^2 = 0$

$(x-4 + y -1)(x-4-y+1) = 0$

$x+y-4+1 = 0\,\,$and$\,\,x-y -4 +1 = 0$

$\therefore x+y = 5 \,\,$and$\,\, x-y = 3$

locus (1 Viewer)

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