# #x+-y = 0# are asymptotes to the family of Rectangular Hyperbolas (RH) #x^2-y^2=+-c^2#. How do you prove that the multitude of straight lines #x+-y=a# are asymptotes to the RH family?

##### 1 Answer

Answer, a mon avis. Perhaps, this could possibly be disproved, in another answer. Please avoid editing my answer.

#### Explanation:

If

as

respectively.

https://www.reddit.com/r/askscience/comments/512ts7/why_do_parallel_lines_meet_at_infinity/

See graphs for convergence to point at

direction, as we advance for higher r.

Graph near origin, for Q_1 ( similar graphs can be created for other

quadrants):

graph{((x^2-y^2)^2-1)((x^2-y^2)^2-9)(x-y-1)(x-y+1)(x-y-4)(x-y+4)(x-y)=0}

Graph for r > 10000:

graph{(x^2-y^2-1)(x^2-y^2-9)(x-y-1)(x-y+1)(x-y-4)(x-y+4)(x-y)=0[0 20000 0 10000]}

Observe that scaling produces alignment, upon marching to

the direction