Locus of moving point (1 Viewer)

[juantheron]

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http://www.wolframalpha.com/input/?i=\sqrt{(x+1)^2+y^2}+\sqrt{(x-1)^2+y^2}+=+1





Someone Explain me, Thanks

 

[InteGrand]

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http://www.wolframalpha.com/input/?i=\sqrt{(x+1)^2+y^2}+\sqrt{(x-1)^2+y^2}+=+1





Someone Explain me, Thanks

 

[Paradoxica]

And since we are assuming Euclidean Geometry anyway, no technicalities from Hyperbolic Geometry/Elliptical Geometry is allowed.

 

[juantheron]

Thanks InteGrand.

But when we solve Then I am getting Hyperbola. Where i have done wrong in my calculation

 

[juantheron]

To Paradoxica I did not understand it.

Would you like to explain me in detail, Thanks

 

[Nailgun]

Thanks InteGrand.

But when we solve Then I am getting Hyperbola. Where i have done wrong in my calculation

I think what they are saying is that your assumption that PA + PB = 1 is incorrect intrinsically, as it is not possible for PA + PB =1 if A and B are points you describe

 

[Paradoxica]

Thanks InteGrand.

But when we solve Then I am getting Hyperbola. Where i have done wrong in my calculation

This "hyperbola" is an extraneous locus that does not satisfy your original described relation.

Think of it like this:

 

[Paradoxica]

upon further investigation, my explanation is verified.

Juantheron, you are essentially squaring both sides of the equation you have constructed.

However, this is not valid, as you originally start out with x = -y

Squaring would then yield x^2 = y^2

And then you are solving for x = y

Which is not what you began with.

 

[Paradoxica]

Okay, after careful observation, this is your error:

you began with

a=b

then said

ac=bc

and then deduced something similar to

c=0

which is not true, as you only began with

a=b

 

[juantheron]

Thanks Paradoxica for Nice explanation.

 

[Tonic Note]

https://45.media.tumblr.com/46a62b93c419fb682b5f066ed1f3a32f/tumblr_o42htzdsWu1v9kamgo1_400.gif