SOLUTION: Find the equation of the locus of a point p (x,y) when: 1. the distance of P from the line y=-5 is three quarters of its distance from the line x = 2 2. The distacne of P fro

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Question 1011590: Find the equation of the locus of a point p (x,y) when:
1. the distance of P from the line y=-5 is three quarters of its distance from the line x = 2
2. The distacne of P from the line x= -3 is two fifths of its distance from the line y= -1

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
The two questions are very much alike. Question number 1 gives the horizontal line y=-5 and the vertical line x=2; these are the more general points (x,-5) and (2,y). Fit the description into the Distance Formula:







Simplify into the two equations in whatever form you want.
-


------one of the lines
-



-----------other line
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.
Find the equation of the locus of a point p (x,y) when:
1. the distance of P from the line y=-5 is three quarters of its distance from the line x = 2
2. The distance of P from the line x= -3 is two fifths of its distance from the line y= -1
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1. The locus for #1 is the straight line passing through the point (x,y) = (2,-5) and having the slope :
   y + 5 = .(x-2),    or    y = 0.75x -  - 5,   or   y = 0.75 - 6.5.

   Make a sketch. Draw the coordinate axes. Draw the line x = 2 and the line y = -5. Then draw your line.


2. Try to do it by analogy with the #1.

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Comment from student: When i tried to do the second question, i could not achieve the answer. Can u show me step by step explanation??
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OK, let's do it.

2. The locus for #2 is the straight line passing through the point (x,y) = (-3,-1) and having the slope :
   y + 1 = .(x+3),    or    y = x +  - 1,   or   y = x + 6.5.

   Make a sketch. Draw the coordinate axes. Draw the line x =-3 and the line y = -1. Then draw your line. 
   Put the point P on the line. Then mark those distances dx and dy. Then think.


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