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f1player

Junior Member
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Feb 25, 2005
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I have a couple of questions, for which I can't get the correct answer for:

1. Find the locus of a point P in the plane such that its distance from the point F(4.0) is always 2/3 of its distance from the line x-9=0

2. Find the locus of a point P in the plane which moves such that the difference of its distances from the points A(-6,0) and B(6,0) is 6

3. Find the locus of a point P in the plane which moves such that its distance from the point F(5,2) is always equal to its distance from the line x=1

This last one is probably the easiest from these three here, but I still can't get the correct anwer.

Maybe the answers are wrong??

The answers are:

1. x^2/36 + y^2/20 = 1

2. x^2/9 - y^2/27 = 1

3. (y-2)^2 = 8(x-3)

I can't seem to get any of these 3 answers for the questions above. Any help would be appreciated
 
These look like applications of the Distance Formula. For instance, the first one would involve:

. . . . .sqrt[(x - 4)<sup>2</sup> + (y - 0)<sup>2</sup>] = (2/3)sqrt[(x - 9)<sup>2</sup> + (y - y)<sup>2</sup>]

What have you tried? How far have you gotten?

Thank you.

Eliz.
 
Ok, so far I've tried:

For question 1:

sqrt[(x-4)^2+(y-0)^2] = 2/3sqrt[(x-9)^2+(y-0)^2

Simplifying: x^2 - 8x +16+y^2 = 4/9 (x^2 -18x+81+y^2)

x^2 - 8x +16+y^2 = (4/9)x^2 -8x+36+(4/9)y^2

(5/9)x^2 -20 + (5/9)y^2= 0

(5/9)x^2 + (5/9)y^2 = 20

(x^2/36) + (y^2/36) = 1

Is that right? The answer is different from the answer given in the book
 
If the line is of the form "x = 9", then how do you get that y is fixed at zero? Think about finding the distance between some point and this line. Does the value of y enter into things at all? Shouldn't the set-up be as I gave it to you earlier?

Eliz.
 
Yes, you are right!

I can't belive I let y=0 in that equation!!

Anyway,now I got the right answer, finally...

But I'm still having a little trouble with question 2

So far I got:


sqrt[(x+6)^2 + (y-0)^2] = 6 + sqrt[(x-6)^2 + (y-0)^2]

Now I'm not sure how to simplify this: This is what I did

x^2 +12x +36 +y^2 = 36 + x^2 -12x +36 +y^2

Then, simplifying this further just gives: x = 1.5, which is completely wrong!!
 
x^2 +12x +36 +y^2 = (6 + sqrt[(x-6)^2 + y^2])(6 + sqrt[(x-6)^2 + y^2])
 
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