## 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.

1. anonymous

why is the point moving..lol..??

2. anonymous

@surjithayer

3. jim_thompson5910

let P be the point (x,y) if A is (0,0) what is the slope of line AP ?

4. anonymous

|dw:1443232316357:dw|

5. jim_thompson5910

we'll stick with y/x what is the slope of BP ?

6. anonymous

|dw:1443232412944:dw|

7. jim_thompson5910

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

surjithayer I'm not sure why you squared both sides

9. anonymous

|dw:1443232684745:dw|

10. jim_thompson5910

11. jim_thompson5910

any point along the horizontal line y = 6 will work as long as x is not 0

12. anonymous

woow really thanks

13. anonymous

but y was the point moving ..lol

14. anonymous

o thats not really a question... im just curious ...

15. anonymous

y=-2 is not working.

16. anonymous

only y=6

17. jim_thompson5910

surjithayer like I said, I'm not sure why you squared both sides. You introduced an extraneous solution

18. jim_thompson5910

the point moves to create the entire line

19. jim_thompson5910

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

i was thinking of absolute slope but i was wrong.

21. anonymous

so the locus is like the radius

22. jim_thompson5910

in this case, the locus is the entire line generated by every point that makes up the line

23. jim_thompson5910

each point P on this line satisfies the condition that slope of AP = (1/2)*(slope of BP)

24. jim_thompson5910

try a few points out like P = (2,6) or P = (7,6)

25. anonymous

like this |dw:1443233581868:dw|

26. jim_thompson5910

if P were (2,6), what's the slope of AP ?

27. DanJS

interesting problem

28. DanJS

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

|dw:1443238354064:dw|

30. DanJS

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

maybe

32. anonymous

o sorry i fall asleep

33. anonymous

i review and its more clear thanks guys