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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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.

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

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|dw:1443232316357:dw|
we'll stick with y/x what is the slope of BP ?
|dw:1443232412944:dw|
`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
surjithayer I'm not sure why you squared both sides
|dw:1443232684745:dw|
yep y = 6 is your answer
any point along the horizontal line y = 6 will work as long as x is not 0
woow really thanks
but y was the point moving ..lol
o thats not really a question... im just curious ...
y=-2 is not working.
only y=6
surjithayer like I said, I'm not sure why you squared both sides. You introduced an extraneous solution
the point moves to create the entire line
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
i was thinking of absolute slope but i was wrong.
so the locus is like the radius
in this case, the locus is the entire line generated by every point that makes up the line
each point P on this line satisfies the condition that slope of AP = (1/2)*(slope of BP)
try a few points out like P = (2,6) or P = (7,6)
like this |dw:1443233581868:dw|
if P were (2,6), what's the slope of AP ?
interesting problem
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
|dw:1443238354064:dw|
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
maybe
o sorry i fall asleep
i review and its more clear thanks guys

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