Thread: Sketch a graph for all (x,y) that are related to the point (1,0)

Consider the real plane, ℝ². Define the relation S on ℝ² by:

(x,y)S(u,v) when x² + y² = u² + v²


(a) Sketch a graph for all (x,y) that are related to the point (1,0)

My attempt:

I think the answer is x=1 since the graph of x=1 intersects the point (1,0) and all circles with a radius of 1 or higher.

Or do I need to sketch a graph that intersects (1,0) and ALL circles of any given radius.

Or it something more simple that i'm not thinking about

Thanks!

Originally Posted by yoman360

Consider the real plane, ℝ². Define the relation S on ℝ² by: (x,y)S(u,v) when x² + y² = u² + v²
(a) Sketch a graph for all (x,y) that are related to the point (1,0)

Question: Is it true that true?

What about .

And if , is it true that true?

Originally Posted by Plato

Question: Is it true that true?

yes, because 1² + 0² = 0² + 1² ==> 1 = 1

Originally Posted by Plato

What about .

No because 1 = 1

Originally Posted by Plato

And if , is it true that true?

oh i see so the answer is the sketch of the graph x²+y² = 1