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anonymous

  • one year ago

Find the equation of the locus of a point which moves so that its distance from the line 6x+2y=13 is always twice its distance from the line y=3x+8

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  1. anonymous
    • one year ago
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    @chris00 @welshfella

  2. anonymous
    • one year ago
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    ok u can leave all taught .. comments.. and i will get back to it when my class is over..which would be in the next 4 hours time.. but right now i have to go get ready to leave home to go school

  3. welshfella
    • one year ago
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    ok well i have to leave for a while anyway but i'll get back to it

  4. anonymous
    • one year ago
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    ok cool

  5. welshfella
    • one year ago
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    ok the sketch looks like this |dw:1444396674018:dw|

  6. welshfella
    • one year ago
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    the locus looks like the middle line which intersects the 2 given lines.

  7. welshfella
    • one year ago
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    We can use the distance formula mentioned bu chris00 is the last question the ditance from any point on the locus is 2 times bigger from the line 6x + 2y = 13 than it is from y = 3x + 8

  8. welshfella
    • one year ago
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    |dw:1444396944703:dw|

  9. welshfella
    • one year ago
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    writing them in the required form for the formula we hav -3x + y - 6.5= 0 and -3x + y - 8 = 0 so plugging these into the distance formulas and since one distance is twice the other;- 3x + y - 6.5 = 2 * (-3x + y - 8) --------------- --------------- sqrt(3^2 + 1^2 ) sqrt (-3^2 + 1^2) since the denominators are the same;- 3x + y - 6.5 = -6x + 2y - 16 simplify this and you have the answer

  10. welshfella
    • one year ago
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    * typo at the start of the second line - that should be 3x NOT -3x

  11. anonymous
    • one year ago
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    6x+2y-13=0 and 3x-y+8=0

  12. anonymous
    • one year ago
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    2(6x+2y-13)/sq.rt (6^2+2^2) 2(6x+2y-13)/sq.rt(40)

  13. anonymous
    • one year ago
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    3x-y+8/sqrt (3^2+(-1)^2) 3x-y+8/sqrt 10

  14. welshfella
    • one year ago
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    3x + y - 6.5 = -6x + 2y - 16 9x - y = -9.5 or 18x - 2y = -19

  15. welshfella
    • one year ago
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    - that is the equation of the locus

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