In the coordinate plane $xOy$ you have drawn parabola $y=x^2$. Now delete the coordinate axes. Using a straightedge and a compass reconstruct coordinate axes.
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David G. Stork
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Djole St
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Ummm... draw a line tangent to the apex. Then draw a line perpendicular to that line, through the apex. – David G. Stork Nov 27 '19 at 23:17
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3Yes, but how to find the apex without the axes? – Bernard Nov 27 '19 at 23:18
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I like the wikipedia entry for "parabola". Have you learned how to find the locus and directrix for a given parabola? – Andrew Chin Nov 27 '19 at 23:29
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Do you mean "ruler" or "straightedge." A ruler allows us to measure lengths and makes the problem easier. – B. Goddard Nov 27 '19 at 23:31
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Hint: Draw any two parallel chords. Their midpoints determine a line parallel to the axis.
Can you continue?
Blue
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5Thank you very much, I just finished construction! Let p be the red line form above, all I need is to draw perpendicular line to it. Midpoint of that line lies on $y$ axis. Then I will draw $y$ axis, and after that $x$ axis.
I think this is the right solution.
– Djole St Nov 28 '19 at 09:52 -
@DjoleSt: Congratulations! That is correct. ... I suggest you write your comment into an answer so that we can upvote your success. You could/should also accept it. – Blue Nov 28 '19 at 13:06
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