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anonymous

  • one year ago

A point P moves so that the slope of AP is half that of BP. Where A is (0,0) and B is (0,-6). Find the equation of the locus.

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  1. anonymous
    • one year ago
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    why is the point moving..lol..??

  2. anonymous
    • one year ago
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    @surjithayer

  3. jim_thompson5910
    • one year ago
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    let P be the point (x,y) if A is (0,0) what is the slope of line AP ?

  4. anonymous
    • one year ago
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    |dw:1443232316357:dw|

  5. jim_thompson5910
    • one year ago
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    we'll stick with y/x what is the slope of BP ?

  6. anonymous
    • one year ago
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    |dw:1443232412944:dw|

  7. jim_thompson5910
    • one year ago
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    `the slope of AP is half that of BP` so \[\Large \text{slope of AP} = \frac{1}{2}\times\text{slope of BP}\] \[\Large \frac{y}{x}= \frac{1}{2}\times\frac{y+6}{x}\] solve for y

  8. jim_thompson5910
    • one year ago
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    surjithayer I'm not sure why you squared both sides

  9. anonymous
    • one year ago
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    |dw:1443232684745:dw|

  10. jim_thompson5910
    • one year ago
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    yep y = 6 is your answer

  11. jim_thompson5910
    • one year ago
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    any point along the horizontal line y = 6 will work as long as x is not 0

  12. anonymous
    • one year ago
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    woow really thanks

  13. anonymous
    • one year ago
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    but y was the point moving ..lol

  14. anonymous
    • one year ago
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    o thats not really a question... im just curious ...

  15. anonymous
    • one year ago
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    y=-2 is not working.

  16. anonymous
    • one year ago
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    only y=6

  17. jim_thompson5910
    • one year ago
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    surjithayer like I said, I'm not sure why you squared both sides. You introduced an extraneous solution

  18. jim_thompson5910
    • one year ago
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    the point moves to create the entire line

  19. jim_thompson5910
    • one year ago
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    imagine you had this locus: the set of all points equidistant from a fixed point that's a circle. The moving point P would circle around the center. As the point moves, it creates the locus

  20. anonymous
    • one year ago
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    i was thinking of absolute slope but i was wrong.

  21. anonymous
    • one year ago
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    so the locus is like the radius

  22. jim_thompson5910
    • one year ago
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    in this case, the locus is the entire line generated by every point that makes up the line

  23. jim_thompson5910
    • one year ago
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    each point P on this line satisfies the condition that slope of AP = (1/2)*(slope of BP)

  24. jim_thompson5910
    • one year ago
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    try a few points out like P = (2,6) or P = (7,6)

  25. anonymous
    • one year ago
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    like this |dw:1443233581868:dw|

  26. jim_thompson5910
    • one year ago
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    if P were (2,6), what's the slope of AP ?

  27. DanJS
    • one year ago
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    interesting problem

  28. DanJS
    • one year ago
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    since A and B have the same x-value, you can see the locus should be a horizontal line at double the vertical distance of AtoB, makes sense, in that case, both have the same change in x, and the change in y is always double for B compared to A

  29. DanJS
    • one year ago
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    |dw:1443238354064:dw|

  30. DanJS
    • one year ago
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    What is the relationship between the rate of change of one of the angles w.r.t. time and the rate of change of the position of P

  31. DanJS
    • one year ago
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    maybe

  32. anonymous
    • one year ago
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    o sorry i fall asleep

  33. anonymous
    • one year ago
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    i review and its more clear thanks guys

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