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

Algebra ->  Quadratic-relations-and-conic-sections -> 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      Log On


   

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) About Me  (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:



sqrt%28%28y%2B5%29%5E2%29=%283%2F4%29sqrt%28%28x-2%29%5E2%29

y%2B5=0%2B-+%283%2F4%29%28x-2%29

Simplify into the two equations in whatever form you want.
-
y%2B5=-%283%2F4%29%28x-2%29
y=-%283%2F4%29x%2B3%2F2-5
highlight%28y=-%283%2F4%29x-7%2F2%29------one of the lines
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y%2B5=%283%2F4%29%28x-2%29
y%2B5=%283%2F4%29x-3%2F2
y=%283%2F4%29x-3%2F2-10%2F2
highlight%28y=%283%2F4%29x-13%2F2%29-----------other line

Answer by ikleyn(52790) About Me  (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 3%2F4:
   y + 5 = 3%2F4.(x-2),    or    y = 0.75x - 3%2F2 - 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 5%2F2:
   y + 1 = 5%2F2.(x+3),    or    y = 5%2F2x + 15%2F2 - 1,   or   y = 5%2F2x + 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.