Question 42839
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what can be said of points with equal abscissa? 

"Abscissa" is a fancy name for the 1st coordinate,
or "x-coordinate"

Let's plot some and see.  Below I have plotted (3,7),
(3,3), (3,-4) and (3,-8), all having the same 
abscissa, 3.

{{{ graph( 400, 400, -10, 10, -10, 10, 3+sqrt(.05-(x-3)^2), 3-sqrt(.05-(x-3)^2), 7+sqrt(.05-(x-3)^2), 7-sqrt(.05-(x-3)^2), -8+sqrt(.05-(x-3)^2), -8-sqrt(.05-(x-3)^2), -4+sqrt(.05-(x-3)^2), -4-sqrt(.05-(x-3)^2), sqrt(.05-(x-3)^2), -sqrt(.05-(x-3)^2) )  }}}

Notice that they all lie on the same vertical line.

{{{ graph( 400, 400, -10, 10, -10, 10, 9999(x-3), 3+sqrt(.05-(x-3)^2), 3-sqrt(.05-(x-3)^2), 7+sqrt(.05-(x-3)^2), 7-sqrt(.05-(x-3)^2), -8+sqrt(.05-(x-3)^2), -8-sqrt(.05-(x-3)^2), -4+sqrt(.05-(x-3)^2), -4-sqrt(.05-(x-3)^2), sqrt(.05-(x-3)^2), -sqrt(.05-(x-3)^2) )  }}}

Incidentally the equation of that vertical line is 
simply this:  

            x = 3 

----------------------------------------------------
with equal ordinates?

"Ordinate" is a fancy name for the 2nd coordinate, 
or "y-coordinate"

Let's plot some and see.  Below I have plotted (-6,-4),
(3,-4), (4,-4) and (7,-4), all having the same 
ordinate, -4.

{{{ graph( 400, 400, -10, 10, -10, 10, -4+sqrt(.05-(x-7)^2), -4-sqrt(.05-(x-7)^2), -4+sqrt(.05-(x-4)^2), -4-sqrt(.05-(x-4)^2), -4+sqrt(.05-(x-3)^2), -4-sqrt(.05-(x-3)^2), -4+sqrt(.05-(x+6)^2), -4-sqrt(.05-(x+6)^2), -4+sqrt(.05-(x+8)^2), -4-sqrt(.05-(x+8)^2) )  }}}

Notice that they all lie on the same horizontal 
line.

{{{ graph( 400, 400, -10, 10, -10, 10, -4, -4+sqrt(.05-(x-7)^2), -4-sqrt(.05-(x-7)^2), -4+sqrt(.05-(x-4)^2), -4-sqrt(.05-(x-4)^2), -4+sqrt(.05-(x-3)^2), -4-sqrt(.05-(x-3)^2), -4+sqrt(.05-(x+6)^2), -4-sqrt(.05-(x+6)^2), -4+sqrt(.05-(x+8)^2), -4-sqrt(.05-(x+8)^2) )  }}}

Incidentally the equation of that horizontal line is 
simply this:  

            y = -4 

Edwin</pre>