anonymous
  • anonymous
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
Mathematics
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
@chris00 @welshfella
anonymous
  • anonymous
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
welshfella
  • welshfella
ok well i have to leave for a while anyway but i'll get back to it

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anonymous
  • anonymous
ok cool
welshfella
  • welshfella
ok the sketch looks like this |dw:1444396674018:dw|
welshfella
  • welshfella
the locus looks like the middle line which intersects the 2 given lines.
welshfella
  • welshfella
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
welshfella
  • welshfella
|dw:1444396944703:dw|
welshfella
  • welshfella
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
welshfella
  • welshfella
* typo at the start of the second line - that should be 3x NOT -3x
anonymous
  • anonymous
6x+2y-13=0 and 3x-y+8=0
anonymous
  • anonymous
2(6x+2y-13)/sq.rt (6^2+2^2) 2(6x+2y-13)/sq.rt(40)
anonymous
  • anonymous
3x-y+8/sqrt (3^2+(-1)^2) 3x-y+8/sqrt 10
welshfella
  • welshfella
3x + y - 6.5 = -6x + 2y - 16 9x - y = -9.5 or 18x - 2y = -19
welshfella
  • welshfella
- that is the equation of the locus

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